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Mathematics Subject Classification – Analysis

REAL FUNCTIONS

 AMS: 26       All of this section
AMS: 26-XX    Not classified at a more specific level
  • AMS: 26Axx    Functions of one variable
    AMS: 26A*     (including sub-levels)
    • AMS: 26A03    Foundations: limits and generalizations, elementary topology of the line
    • AMS: 26A06    One-variable calculus
    • AMS: 26A09    Elementary functions
    • AMS: 26A12    Rate of growth of functions, orders of infinity, slowly varying functions
    • AMS: 26A15    Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
    • AMS: 26A16    Lipschitz (Hölder) classes
    • AMS: 26A18    Iteration
    • AMS: 26A21    Classification of real functions; Baire classification of sets and functions
    • AMS: 26A24    Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems
    • AMS: 26A27    Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
    • AMS: 26A30    Singular functions, Cantor functions, functions with other special properties
    • AMS: 26A33    Fractional derivatives and integrals
    • AMS: 26A39    Denjoy and Perron integrals, other special integrals
    • AMS: 26A42    Integrals of Riemann, Stieltjes and Lebesgue type
    • AMS: 26A48    Monotonic functions, generalizations
    • AMS: 26A51    Convexity, generalizations
    • AMS: 26A99    None of the above, but in this section
  • AMS: 26Bxx    Functions of several variables
    AMS: 26B*     (including sub-levels)
    • AMS: 26B05    Continuity and differentiation questions
    • AMS: 26B10    Implicit function theorems, Jacobians, transformations with several variables
    • AMS: 26B12    Calculus of vector functions
    • AMS: 26B15    Integration: length, area, volume
    • AMS: 26B20    Integral formulas (Stokes, Gauss, Green, etc.)
    • AMS: 26B25    Convexity, generalizations
    • AMS: 26B30    Absolutely continuous functions, functions of bounded variation
    • AMS: 26B35    Special properties of functions of several variables, Hölder conditions, etc.
    • AMS: 26B99    None of the above, but in this section
  • AMS: 26Cxx    Polynomials, rational functions
    AMS: 26C*     (including sub-levels)
  • AMS: 26Dxx    Inequalities
    AMS: 26D*     (including sub-levels)
    • AMS: 26D05    Inequalities for trigonometric functions and polynomials
    • AMS: 26D10    Inequalities involving derivatives and differential and integral operators
    • AMS: 26D15    Inequalities for sums, series and integrals
    • AMS: 26D20    Other analytical inequalities
  • AMS: 26Exx    Miscellaneous topics
    AMS: 26E*     (including sub-levels)

MEASURE AND INTEGRATION

 AMS: 28       All of this section
AMS: 28-XX    Not classified at a more specific level
  • AMS: 28Axx    Classical measure theory
    AMS: 28A*     (including sub-levels)
    • AMS: 28A05    Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets
    • AMS: 28A10    Real- or complex-valued set functions
    • AMS: 28A12    Contents, measures, outer measures, capacities
    • AMS: 28A15    Abstract differentiation theory, differentiation of set functions
    • AMS: 28A20    Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
    • AMS: 28A25    Integration with respect to measures and other set functions
    • AMS: 28A33    Spaces of measures, convergence of measures
    • AMS: 28A35    Measures and integrals in product spaces
    • AMS: 28A50    Integration and disintegration of measures
    • AMS: 28A75    Length, area, volume, other geometric measure theory
    • AMS: 28A78    Hausdorff and packing measures
    • AMS: 28A80    Fractals
  • AMS: 28Bxx    Set functions, measures and integrals with values in abstract spaces
    AMS: 28B*     (including sub-levels)
    • AMS: 28B05    Vector-valued set functions, measures and integrals
    • AMS: 28B20    Set-valued set functions and measures; integration of set-valued functions; measurable selections
  • AMS: 28Cxx    Set functions and measures on spaces with additional structure
    AMS: 28C*     (including sub-levels)
    • AMS: 28C05    Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
    • AMS: 28C10    Set functions and measures on topological groups, Haar measures, invariant measures
    • AMS: 28C20    Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
  • AMS: 28Dxx    Measure-theoretic ergodic theory
    AMS: 28D*     (including sub-levels)
    • AMS: 28D05    Measure-preserving transformations
    • AMS: 28D10    One-parameter continuous families of measure-preserving transformations
    • AMS: 28D15    General groups of measure-preserving transformations
    • AMS: 28D20    Entropy and other invariants
    • AMS: 28D99    None of the above, but in this section
  • AMS: 28Exx    Miscellaneous topics in measure theory
    AMS: 28E*     (including sub-levels)

FUNCTIONS OF A COMPLEX VARIABLE

 AMS: 30       All of this section
AMS: 30-XX    Not classified at a more specific level
  • AMS: 30Axx    General properties
    AMS: 30A*     (including sub-levels)
    • AMS: 30A05    Monogenic properties of complex functions (including polygenic and areolar monogenic functions)
    • AMS: 30A99    None of the above, but in this section
  • AMS: 30Bxx    Series expansions
    AMS: 30B*     (including sub-levels)
    • AMS: 30B30    Boundary behavior of power series, over-convergence
    • AMS: 30B50    Dirichlet series and other series expansions, exponential series
    • AMS: 30B70    Continued fractions
  • AMS: 30Cxx    Geometric function theory
    AMS: 30C*     (including sub-levels)
    • AMS: 30C10    Polynomials
    • AMS: 30C15    Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral)
    • AMS: 30C20    Conformal mappings of special domains
    • AMS: 30C30    Numerical methods in conformal mapping theory
    • AMS: 30C35    General theory of conformal mappings
    • AMS: 30C40    Kernel functions and applications
    • AMS: 30C45    Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
    • AMS: 30C50    Coefficient problems for univalent and multivalent functions
    • AMS: 30C55    General theory of univalent and multivalent functions
    • AMS: 30C62    Quasiconformal mappings in the plane
    • AMS: 30C65    Quasiconformal mappings in $R^n$, other generalizations
    • AMS: 30C75    Extremal problems for conformal and quasiconformal mappings, other methods
    • AMS: 30C80    Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination
    • AMS: 30C85    Capacity and harmonic measure in the complex plane
    • AMS: 30C99    None of the above, but in this section
  • AMS: 30Dxx    Entire and meromorphic functions, and related topics
    AMS: 30D*     (including sub-levels)
    • AMS: 30D05    Functional equations in the complex domain, iteration and composition of analytic functions
    • AMS: 30D15    Special classes of entire functions and growth estimates
    • AMS: 30D20    Entire functions, general theory
    • AMS: 30D30    Meromorphic functions, general theory
    • AMS: 30D35    Distribution of values, Nevanlinna theory
    • AMS: 30D45    Bloch functions, normal functions, normal families
  • AMS: 30Exx    Miscellaneous topics of analysis in the complex domain
    AMS: 30E*     (including sub-levels)
    • AMS: 30E05    Moment problems, interpolation problems
    • AMS: 30E10    Approximation in the complex domain
    • AMS: 30E15    Asymptotic representations in the complex domain
    • AMS: 30E20    Integration, integrals of Cauchy type, integral representations of analytic functions
    • AMS: 30E25    Boundary value problems
    • AMS: 30E99    None of the above, but in this section
  • AMS: 30Fxx    Riemann surfaces
    AMS: 30F*     (including sub-levels)
  • AMS: 30Gxx    Generalized function theory
    AMS: 30G*     (including sub-levels)
    • AMS: 30G06    Non-Archimedean function theory
    • AMS: 30G20    Generalizations of Bers or Vekua type (pseudoanalytic, $p$-analytic, etc.)
    • AMS: 30G30    Other generalizations of analytic functions (including abstract-valued functions)
    • AMS: 30G35    Functions of hypercomplex variables and generalized variables
  • AMS: 30Hxx    Spaces and algebras of analytic functions
    AMS: 30H*     (including sub-levels)
  • AMS: 30Jxx    Function theory on the disc
    AMS: 30J*     (including sub-levels)
  • AMS: 30Kxx    Universal holomorphic functions
    AMS: 30K*     (including sub-levels)
  • AMS: 30Lxx    Analysis on metric spaces
    AMS: 30L*     (including sub-levels)

POTENTIAL THEORY

 AMS: 31       All of this section
AMS: 31-XX    Not classified at a more specific level

SEVERAL COMPLEX VARIABLES AND ANALYTIC SPACES

 AMS: 32       All of this section
AMS: 32-XX    Not classified at a more specific level

SPECIAL FUNCTIONS

 AMS: 33       All of this section
AMS: 33-XX    Not classified at a more specific level
  • AMS: 33Bxx    Elementary classical functions
    AMS: 33B*     (including sub-levels)
    • AMS: 33B10    Exponential and trigonometric functions
    • AMS: 33B15    Gamma, beta and polygamma functions
    • AMS: 33B20    Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)
  • AMS: 33Cxx    Hypergeometric functions
    AMS: 33C*     (including sub-levels)
    • AMS: 33C05    Classical hypergeometric functions, $_2F_1$
    • AMS: 33C10    Bessel and Airy functions, cylinder functions, $_0F_1$
    • AMS: 33C20    Generalized hypergeometric series, $_pF_q$
    • AMS: 33C45    Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
    • AMS: 33C47    Other special orthogonal polynomials and functions
    • AMS: 33C55    Spherical harmonics
    • AMS: 33C65    Appell, Horn and Lauricella functions
    • AMS: 33C75    Elliptic integrals as hypergeometric functions
    • AMS: 33C80    Connections with groups and algebras, and related topics
  • AMS: 33Dxx    Basic hypergeometric functions
    AMS: 33D*     (including sub-levels)
    • AMS: 33D05    $q$-gamma functions, $q$-beta functions and integrals
    • AMS: 33D15    Basic hypergeometric functions in one variable, $_r\phi_s$
    • AMS: 33D45    Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
    • AMS: 33D52    Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)
    • AMS: 33D67    Basic hypergeometric functions associated with root systems
    • AMS: 33D80    Connections with quantum groups, Chevalley groups, $p$-adic groups, Hecke algebras, and related topics
  • AMS: 33Exx    Other special functions
    AMS: 33E*     (including sub-levels)
    • AMS: 33E05    Elliptic functions and integrals
    • AMS: 33E17    Painlevé-type functions
    • AMS: 33E20    Other functions defined by series and integrals
    • AMS: 33E30    Other functions coming from differential, difference and integral equations
  • AMS: 33Fxx    Computational aspects
    AMS: 33F*     (including sub-levels)

ORDINARY DIFFERENTIAL EQUATIONS

 AMS: 34       All of this section
AMS: 34-XX    Not classified at a more specific level

PARTIAL DIFFERENTIAL EQUATIONS

 AMS: 35       All of this section
AMS: 35-XX    Not classified at a more specific level
  • AMS: 35Axx    General theory
    AMS: 35A*     (including sub-levels)
  • AMS: 35Bxx    Qualitative properties of solutions
    AMS: 35B*     (including sub-levels)
  • AMS: 35Cxx    Representations of solutions
    AMS: 35C*     (including sub-levels)
  • AMS: 35Dxx    Generalized solutions of partial differential equations
    AMS: 35D*     (including sub-levels)
    • AMS: 35D99    None of the above, but in this section
  • AMS: 35Exx    Equations and systems with constant coefficients
    AMS: 35E*     (including sub-levels)
  • AMS: 35Fxx    General first-order equations and systems
    AMS: 35F*     (including sub-levels)
    • AMS: 35F05    General theory of linear first-order PDE
    • AMS: 35F10    Initial value problems for linear first-order PDE, linear evolution equations
    • AMS: 35F15    Boundary value problems for linear first-order PDE
    • AMS: 35F20    General theory of nonlinear first-order PDE
    • AMS: 35F25    Initial value problems for nonlinear first-order PDE, nonlinear evolution equations
    • AMS: 35F30    Boundary value problems for nonlinear first-order PDE
    • AMS: 35F99    None of the above, but in this section
  • AMS: 35Gxx    General higher-order equations and systems
    AMS: 35G*     (including sub-levels)
    • AMS: 35G05    General theory of linear higher-order PDE
    • AMS: 35G10    Initial value problems for linear higher-order PDE, linear evolution equations
    • AMS: 35G15    Boundary value problems for linear higher-order PDE
    • AMS: 35G20    General theory of nonlinear higher-order PDE
    • AMS: 35G25    Initial value problems for nonlinear higher-order PDE, nonlinear evolution equations
    • AMS: 35G30    Boundary value problems for nonlinear higher-order PDE
  • AMS: 35Hxx    Close-to-elliptic equations
    AMS: 35H*     (including sub-levels)
  • AMS: 35Jxx    Partial differential equations of elliptic type
    AMS: 35J*     (including sub-levels)
    • AMS: 35J05    Laplace equation, reduced wave equation (Helmholtz), Poisson equation
    • AMS: 35J10    Schrödinger operator
    • AMS: 35J15    General theory of second-order, elliptic equations
    • AMS: 35J20    Variational methods for second-order, elliptic equations
    • AMS: 35J25    Boundary value problems for second-order, elliptic equations
    • AMS: 35J30    General theory of higher-order, elliptic equations
    • AMS: 35J35    Variational methods for higher-order, elliptic equations
    • AMS: 35J40    Boundary value problems for higher-order, elliptic equations
    • AMS: 35J60    Nonlinear PDE of elliptic type
    • AMS: 35J65    Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE
    • AMS: 35J67    Boundary values of solutions to elliptic PDE
    • AMS: 35J70    Elliptic partial differential equations of degenerate type
    • AMS: 35J99    None of the above, but in this section
  • AMS: 35Kxx    Parabolic equations and systems
    AMS: 35K*     (including sub-levels)
    • AMS: 35K05    Heat equation
    • AMS: 35K10    General theory of second-order, parabolic equations
    • AMS: 35K15    Initial value problems for second-order, parabolic equations
    • AMS: 35K20    Boundary value problems for second-order, parabolic equations
    • AMS: 35K25    General theory of higher-order, parabolic equations
    • AMS: 35K55    Nonlinear PDE of parabolic type
    • AMS: 35K57    Reaction-diffusion equations
    • AMS: 35K60    Nonlinear boundary value problems for linear parabolic PDE; boundary value problems for nonlinear parabolic PDE
    • AMS: 35K65    Parabolic partial differential equations of degenerate type
    • AMS: 35K70    Ultraparabolic, pseudoparabolic PDE, etc.
    • AMS: 35K85    Unilateral problems and variational inequalities for parabolic PDE
    • AMS: 35K90    Abstract parabolic evolution equations
    • AMS: 35K99    None of the above, but in this section
  • AMS: 35Lxx    Partial differential equations of hyperbolic type
    AMS: 35L*     (including sub-levels)
    • AMS: 35L05    Wave equation
    • AMS: 35L10    General theory of second-order, hyperbolic equations
    • AMS: 35L15    Initial value problems for second-order, hyperbolic equations
    • AMS: 35L20    Boundary value problems for second-order, hyperbolic equations
    • AMS: 35L30    Initial value problems for higher-order, hyperbolic equations
    • AMS: 35L40    General theory of hyperbolic systems of first-order PDE
    • AMS: 35L45    Initial value problems for hyperbolic systems of first-order PDE
    • AMS: 35L50    Boundary value problems for hyperbolic systems of first-order PDE
    • AMS: 35L55    Hyperbolic systems of higher-order PDE
    • AMS: 35L60    Nonlinear first-order PDE of hyperbolic type
    • AMS: 35L65    Conservation laws
    • AMS: 35L67    Shocks and singularities
    • AMS: 35L70    Nonlinear second-order PDE of hyperbolic type
    • AMS: 35L75    Nonlinear hyperbolic PDE of higher ($\gtr 2$) order
  • AMS: 35Mxx    Partial differential equations of special type (mixed, composite, etc.)
    AMS: 35M*     (including sub-levels)
  • AMS: 35Nxx    Overdetermined systems
    AMS: 35N*     (including sub-levels)
    • AMS: 35N05    Overdetermined systems with constant coefficients
    • AMS: 35N10    Overdetermined systems with variable coefficients (general)
    • AMS: 35N15    $\overline\partial$-Neumann problem and generalizations; formal complexes
  • AMS: 35Pxx    Spectral theory and eigenvalue problems for partial differential operators
    AMS: 35P*     (including sub-levels)
    • AMS: 35P05    General spectral theory of PDE
    • AMS: 35P10    Completeness of eigenfunctions, eigenfunction expansions for PDO
    • AMS: 35P15    Estimation of eigenvalues, upper and lower bounds
    • AMS: 35P20    Asymptotic distribution of eigenvalues and eigenfunctions for PDO
    • AMS: 35P25    Scattering theory for PDE
    • AMS: 35P30    Nonlinear eigenvalue problems, nonlinear spectral theory for PDO
    • AMS: 35P99    None of the above, but in this section
  • AMS: 35Qxx    Equations of mathematical physics and other areas of application
    AMS: 35Q*     (including sub-levels)
    • AMS: 35Q05    Euler-Poisson-Darboux equation and generalizations
    • AMS: 35Q15    Riemann-Hilbert problems
    • AMS: 35Q30    Stokes and Navier-Stokes equations
    • AMS: 35Q35    Other equations arising in fluid mechanics
    • AMS: 35Q40    Equations from quantum mechanics
    • AMS: 35Q51    Solitons
    • AMS: 35Q53    KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.)
    • AMS: 35Q55    NLS-like (nonlinear Schrödinger) equations
    • AMS: 35Q60    Equations of electromagnetic theory and optics
    • AMS: 35Q74    PDEs in connection with mechanics of deformable solids
    • AMS: 35Q75    PDE in relativity
    • AMS: 35Q99    None of the above, but in this section
  • AMS: 35Rxx    Miscellaneous topics involving partial differential equations
    AMS: 35R*     (including sub-levels)
    • AMS: 35R05    PDE with discontinuous coefficients or data
    • AMS: 35R15    Partial differential equations on infinite-dimensional (e.g. function) spaces (=PDE in infinitely many variables)
    • AMS: 35R20    Partial operator-differential equations (i.e. PDE on finite-dimensional spaces for abstract space valued functions)
    • AMS: 35R25    Improperly posed problems for PDE
    • AMS: 35R30    Inverse problems (undetermined coefficients, etc.) for PDE
    • AMS: 35R35    Free boundary problems for PDE
    • AMS: 35R45    Partial differential inequalities
    • AMS: 35R60    Partial differential equations with randomness
    • AMS: 35R99    None of the above, but in this section
  • AMS: 35Sxx    Pseudodifferential operators and other generalizations of partial differential operators
    AMS: 35S*     (including sub-levels)

DYNAMICAL SYSTEMS AND ERGODIC THEORY

 AMS: 37       All of this section
AMS: 37-XX    Not classified at a more specific level
  • AMS: 37Axx    Ergodic theory
    AMS: 37A*     (including sub-levels)
    • AMS: 37A05    Measure-preserving transformations
    • AMS: 37A15    General groups of measure-preserving transformation
    • AMS: 37A20    Orbit equivalence, cocycles, ergodic equivalence relations
    • AMS: 37A25    Ergodicity, mixing, rates of mixing
    • AMS: 37A30    Ergodic theorems, spectral theory, Markov operators
    • AMS: 37A45    Relations with number theory and harmonic analysis
    • AMS: 37A50    Relations with probability theory and stochastic processes
    • AMS: 37A60    Dynamical systems in statistical mechanics
    • AMS: 37A99    None of the above, but in this section
  • AMS: 37Bxx    Topological dynamics
    AMS: 37B*     (including sub-levels)
  • AMS: 37Cxx    Smooth dynamical systems: general theory
    AMS: 37C*     (including sub-levels)
    • AMS: 37C05    Smooth mappings and diffeomorphisms
    • AMS: 37C10    Vector fields, flows, ordinary differential equations
    • AMS: 37C25    Fixed points, periodic points, fixed-point index theory
    • AMS: 37C29    Homoclinic and heteroclinic orbits
    • AMS: 37C30    Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
    • AMS: 37C40    Smooth ergodic theory, invariant measures
    • AMS: 37C55    Periodic and quasiperiodic flows and diffeomorphisms
    • AMS: 37C70    Attractors and repellers, topological structure
    • AMS: 37C75    Stability theory
    • AMS: 37C80    Symmetries, equivariant dynamical systems
    • AMS: 37C85    Dynamics of group actions other than Z and R, and foliations
    • AMS: 37C99    None of the above, but in this section
  • AMS: 37Dxx    Dynamical systems with hyperbolic behavior
    AMS: 37D*     (including sub-levels)
    • AMS: 37D05    Hyperbolic orbits and sets
    • AMS: 37D15    Morse-Smale systems
    • AMS: 37D20    Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
    • AMS: 37D35    Thermodynamic formalism, variational principles, equilibrium states
    • AMS: 37D40    Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
    • AMS: 37D45    Strange attractors, chaotic dynamics
    • AMS: 37D99    None of the above, but in this section
  • AMS: 37Exx    Low-dimensional dynamical systems
    AMS: 37E*     (including sub-levels)
  • AMS: 37Fxx    Complex dynamical systems
    AMS: 37F*     (including sub-levels)
    • AMS: 37F10    Polynomials; rational maps; entire and meromorphic functions
    • AMS: 37F25    Renormalization
    • AMS: 37F35    Conformal densities and Hausdorff dimension
    • AMS: 37F45    Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
    • AMS: 37F50    Small divisors, rotation domains and linearization; Fatou and Julia sets
    • AMS: 37F75    Holomorphic foliations and vector fields
    • AMS: 37F99    None of the above, but in this section
  • AMS: 37Gxx    Local and nonlocal bifurcation theory
    AMS: 37G*     (including sub-levels)
  • AMS: 37Hxx    Random dynamical systems
    AMS: 37H*     (including sub-levels)
    • AMS: 37H10    Generation, random and stochastic difference and differential equations
    • AMS: 37H15    Multiplicative ergodic theory, Lyapunov exponents
    • AMS: 37h20    Bifurcation theory
    • AMS: 37H99    None of the above, but in this section
  • AMS: 37Jxx    Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
    AMS: 37J*     (including sub-levels)
    • AMS: 37J05    General theory, relations with symplectic geometry and topology
    • AMS: 37J10    Symplectic mappings, fixed points
    • AMS: 37J25    Stability problems
    • AMS: 37J30    Obstructions to integrability (nonintegrability criteria)
    • AMS: 37J35    Completely integrable systems, topological structure of phase space, integration methods
    • AMS: 37J40    Perturbations, normal forms, small divisors, KAM theory, Arnold diffusion
    • AMS: 37J50    Action-minimizing orbits and measures
    • AMS: 37J99    None of the above, but in this section
  • AMS: 37Kxx    Infinite-dimensional Hamiltonian systems
    AMS: 37K*     (including sub-levels)
    • AMS: 37K05    Hamiltonian structures, symmetries, variational principles, conservation laws
    • AMS: 37K10    Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
    • AMS: 37K15    Integration of completely integrable systems by inverse spectral and scattering methods
    • AMS: 37K20    Relations with algebraic geometry, complex analysis, special functions
    • AMS: 37K25    Relations with differential geometry
    • AMS: 37K35    Lie-Bäcklund and other transformations
    • AMS: 37K40    Soliton theory, asymptotic behavior of solutions
    • AMS: 37K45    Stability problems
    • AMS: 37K55    Perturbations, KAM for infinite-dimensional systems
    • AMS: 37K65    Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics
  • AMS: 37Lxx    Infinite-dimensional dissipative dynamical systems
    AMS: 37L*     (including sub-levels)
    • AMS: 37L05    General theory, nonlinear semigroups, evolution equations
    • AMS: 37L50    Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems
    • AMS: 37L55    Infinite-dimensional random dynamical systems; stochastic equations
  • AMS: 37Mxx    Approximation methods and numerical treatment of dynamical systems
    AMS: 37M*     (including sub-levels)
  • AMS: 37Nxx    Applications
    AMS: 37N*     (including sub-levels)
    • AMS: 37N05    Dynamical systems in classical and celestial mechanics
    • AMS: 37N10    Dynamical systems in fluid mechanics, oceanography and meteorology
    • AMS: 37N20    Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
    • AMS: 37N25    Dynamical systems in biology
    • AMS: 37N35    Dynamical systems in control
    • AMS: 37N99    None of the above, but in this section
  • AMS: 37Pxx    Arithmetic and non-Archimedean dynamical systems
    AMS: 37P*     (including sub-levels)

DIFFERENCE AND FUNCTIONAL EQUATIONS

 AMS: 39       All of this section
AMS: 39-XX    Not classified at a more specific level

SEQUENCES, SERIES, SUMMABILITY

 AMS: 40       All of this section
AMS: 40-XX    Not classified at a more specific level

APPROXIMATIONS AND EXPANSIONS

 AMS: 41       All of this section
AMS: 41-XX    Not classified at a more specific level
  • AMS: 41Axx    Approximations and expansions
    AMS: 41A*     (including sub-levels)
    • AMS: 41A05    Interpolation
    • AMS: 41A10    Approximation by polynomials
    • AMS: 41A15    Spline approximation
    • AMS: 41A17    Inequalities in approximation (Bernstein, Jackson, Nikol\cprime ski\u\i-type inequalities)
    • AMS: 41A20    Approximation by rational functions
    • AMS: 41A21    Padé approximation
    • AMS: 41A25    Rate of convergence, degree of approximation
    • AMS: 41A28    Simultaneous approximation
    • AMS: 41A30    Approximation by other special function classes
    • AMS: 41A46    Approximation by arbitrary nonlinear expressions; widths and entropy
    • AMS: 41A50    Best approximation, Chebyshev systems
    • AMS: 41A52    Uniqueness of best approximation
    • AMS: 41A55    Approximate quadratures
    • AMS: 41A60    Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
    • AMS: 41A63    Multidimensional problems
    • AMS: 41A65    Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)

FOURIER ANALYSIS

 AMS: 42       All of this section
AMS: 42-XX    Not classified at a more specific level
  • AMS: 42Axx    Fourier analysis in one variable
    AMS: 42A*     (including sub-levels)
    • AMS: 42A05    Trigonometric polynomials, inequalities, extremal problems
    • AMS: 42A10    Trigonometric approximation
    • AMS: 42A15    Trigonometric interpolation
    • AMS: 42A16    Fourier coefficients, Fourier series of functions with special properties, special Fourier series
    • AMS: 42A20    Convergence and absolute convergence of Fourier and trigonometric series
    • AMS: 42A24    Summability and absolute summability of Fourier and trigonometric series
    • AMS: 42A32    Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
    • AMS: 42A38    Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
    • AMS: 42A45    Multipliers
    • AMS: 42A50    Conjugate functions, conjugate series, singular integrals
    • AMS: 42A55    Lacunary series of trigonometric and other functions; Riesz products
    • AMS: 42A61    Probabilistic methods
    • AMS: 42A63    Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization
    • AMS: 42A65    Completeness of sets of functions
    • AMS: 42A70    Trigonometric moment problems
    • AMS: 42A85    Convolution, factorization
    • AMS: 42A99    None of the above, but in this section
  • AMS: 42Bxx    Fourier analysis in several variables
    AMS: 42B*     (including sub-levels)
  • AMS: 42Cxx    Nontrigonometric Fourier analysis
    AMS: 42C*     (including sub-levels)
    • AMS: 42C05    Orthogonal functions and polynomials, general theory
    • AMS: 42C10    Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
    • AMS: 42C15    Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions
    • AMS: 42C20    Rearrangements and other transformations of Fourier and other orthogonal series
    • AMS: 42C40    Wavelets

ABSTRACT HARMONIC ANALYSIS

 AMS: 43       All of this section
AMS: 43-XX    Not classified at a more specific level
  • AMS: 43Axx    Abstract harmonic analysis
    AMS: 43A*     (including sub-levels)
    • AMS: 43A05    Measures on groups and semigroups, etc.
    • AMS: 43A07    Means on groups, semigroups, etc.; amenable groups
    • AMS: 43A10    Measure algebras on groups, semigroups, etc.
    • AMS: 43A15    $L^p$-spaces and other function spaces on groups, semigroups, etc.
    • AMS: 43A20    $L^1$-algebras on groups, semigroups, etc.
    • AMS: 43A22    Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
    • AMS: 43A25    Fourier and Fourier-Stieltjes transforms on locally compact abelian groups
    • AMS: 43A30    Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
    • AMS: 43A35    Positive definite functions on groups, semigroups, etc.
    • AMS: 43A45    Spectral synthesis on groups, semigroups, etc.
    • AMS: 43A46    Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
    • AMS: 43A50    Convergence of Fourier series and of inverse transforms
    • AMS: 43A62    Hypergroups
    • AMS: 43A65    Representations of groups, semigroups, etc.
    • AMS: 43A70    Analysis on specific locally compact abelian groups
    • AMS: 43A80    Analysis on other specific Lie groups
    • AMS: 43A85    Analysis on homogeneous spaces
    • AMS: 43A90    Spherical functions
    • AMS: 43A95    Categorical methods

INTEGRAL TRANSFORMS, OPERATIONAL CALCULUS

 AMS: 44       All of this section
AMS: 44-XX    Not classified at a more specific level

INTEGRAL EQUATIONS

 AMS: 45       All of this section
AMS: 45-XX    Not classified at a more specific level

FUNCTIONAL ANALYSIS

 AMS: 46       All of this section
AMS: 46-XX    Not classified at a more specific level
  • AMS: 46Axx    Topological linear spaces and related structures
    AMS: 46A*     (including sub-levels)
    • AMS: 46A03    General theory of locally convex spaces
    • AMS: 46A04    Locally convex Fréchet spaces and (DF)-spaces
    • AMS: 46A08    Barrelled spaces, bornological spaces
    • AMS: 46A11    Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
    • AMS: 46A13    Spaces defined by inductive or projective limits (LB, LF, etc.)
    • AMS: 46A16    Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
    • AMS: 46A19    Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than ${\bf R}$, etc.)
    • AMS: 46A20    Duality theory
    • AMS: 46A22    Theorems of Hahn-Banach type; extension and lifting of functionals and operators
    • AMS: 46A30    Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness)
    • AMS: 46A32    Spaces of linear operators; topological tensor products; approximation properties
    • AMS: 46A35    Summability and bases
    • AMS: 46A40    Ordered topological linear spaces, vector lattices
    • AMS: 46A45    Sequence spaces (including Köthe sequence spaces)
    • AMS: 46A50    Compactness in topological linear spaces; angelic spaces, etc.
    • AMS: 46A55    Convex sets in topological linear spaces; Choquet theory
    • AMS: 46A63    Topological invariants ((DN), ($\Omega$), etc.)
    • AMS: 46A99    None of the above, but in this section
  • AMS: 46Bxx    Normed linear spaces and Banach spaces; Banach lattices
    AMS: 46B*     (including sub-levels)
  • AMS: 46Cxx    Inner product spaces and their generalizations, Hilbert spaces
    AMS: 46C*     (including sub-levels)
    • AMS: 46C05    Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
    • AMS: 46C20    Spaces with indefinite inner product (Krein spaces, Pontryagin spaces,...)
    • AMS: 46C99    None of the above, but in this section
  • AMS: 46Exx    Linear function spaces and their duals
    AMS: 46E*     (including sub-levels)
    • AMS: 46E05    Lattices of continuous, differentiable or analytic functions
    • AMS: 46E10    Topological linear spaces of continuous, differentiable or analytic functions
    • AMS: 46E15    Banach spaces of continuous, differentiable or analytic functions
    • AMS: 46E20    Hilbert spaces of continuous, differentiable or analytic functions
    • AMS: 46E22    Hilbert spaces with reproducing kernels (=
    • AMS: 46E25    Rings and algebras of continuous, differentiable or analytic functions
    • AMS: 46E27    Spaces of measures
    • AMS: 46E30    Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
    • AMS: 46E35    Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
    • AMS: 46E40    Spaces of vector- and operator-valued functions
    • AMS: 46E99    None of the above, but in this section
  • AMS: 46Fxx    Distributions, generalized functions, distribution spaces
    AMS: 46F*     (including sub-levels)
    • AMS: 46F05    Topological linear spaces of test functions, distributions and ultradistributions
    • AMS: 46F10    Operations with distributions
    • AMS: 46F12    Integral transforms in distribution spaces
    • AMS: 46F15    Hyperfunctions, analytic functionals
    • AMS: 46F20    Distributions and ultradistributions as boundary values of analytic functions
    • AMS: 46F99    None of the above, but in this section
  • AMS: 46Gxx    Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
    AMS: 46G*     (including sub-levels)
  • AMS: 46Hxx    Topological algebras, normed rings and algebras, Banach algebras
    AMS: 46H*     (including sub-levels)
    • AMS: 46H05    General theory of topological algebras
    • AMS: 46H10    Ideals and subalgebras
    • AMS: 46H15    Representations of topological algebras
    • AMS: 46h20    Structure, classification of topological algebras
    • AMS: 46h25    Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
    • AMS: 46h20    Functional calculus in topological algebras
    • AMS: 46H40    Automatic continuity
    • AMS: 46H70    Nonassociative topological algebras
  • AMS: 46Jxx    Commutative Banach algebras and commutative topological algebras
    AMS: 46J*     (including sub-levels)
    • AMS: 46J05    General theory of commutative topological algebras
    • AMS: 46J10    Banach algebras of continuous functions, function algebras
    • AMS: 46J15    Banach algebras of differentiable or analytic functions, $H^p$-spaces
  • AMS: 46Kxx    Topological (rings and) algebras with an involution
    AMS: 46K*     (including sub-levels)
    • AMS: 46K10    Representations of topological algebras with involution
  • AMS: 46Lxx    Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W$*-) algebras, etc.)
    AMS: 46L*     (including sub-levels)
    • AMS: 46L05    General theory of $C^*$-algebras
    • AMS: 46L07    Operator spaces and completely bounded maps
    • AMS: 46L10    General theory of von Neumann algebras
    • AMS: 46L30    States
    • AMS: 46L35    Classifications of $C^*$-algebras, factors
    • AMS: 46L37    Subfactors and their classification
    • AMS: 46L40    Automorphisms
    • AMS: 46L45    Decomposition theory for $C^*$-algebras
    • AMS: 46L51    Noncommutative measure and integration
    • AMS: 46L52    Noncommutative function spaces
    • AMS: 46L53    Noncommutative probability and statistics
    • AMS: 46L54    Free probability and free operator algebras
    • AMS: 46L55    Noncommutative dynamical systems
    • AMS: 46L57    Derivations, dissipations and positive semigroups in $C^*$-algebras
    • AMS: 46L60    Applications of selfadjoint operator algebras to physics
    • AMS: 46L65    Quantizations, deformations
    • AMS: 46L70    Nonassociative selfadjoint operator algebras
    • AMS: 46L80    $K$-theory and operator algebras (including cyclic theory)
    • AMS: 46L85    Noncommutative topology
    • AMS: 46L87    Noncommutative differential geometry
    • AMS: 46L89    Other ``noncommutative'' mathematics based on $C^*$-algebra theory
    • AMS: 46L99    None of the above, but in this section
  • AMS: 46Mxx    Methods of category theory in functional analysis
    AMS: 46M*     (including sub-levels)
    • AMS: 46M05    Tensor products
    • AMS: 46M10    Projective and injective objects
    • AMS: 46M15    Categories, functors
    • AMS: 46M18    Homological methods (exact sequences, right inverses, lifting, etc.)
    • AMS: 46M20    Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
    • AMS: 46M35    Abstract interpolation of topological vector spaces
    • AMS: 46M40    Inductive and projective limits
  • AMS: 46Nxx    Miscellaneous applications of functional analysis
    AMS: 46N*     (including sub-levels)
    • AMS: 46N10    Applications in optimization, convex analysis, mathematical programming, economics
    • AMS: 46N30    Applications in probability theory and statistics
    • AMS: 46N40    Applications in numerical analysis
    • AMS: 46N50    Applications in quantum physics
    • AMS: 46N55    Applications in statistical physics
    • AMS: 46N60    Applications in biology and other sciences
    • AMS: 46N99    None of the above, but in this section
  • AMS: 46Sxx    Other (nonclassical) types of functional analysis
    AMS: 46S*     (including sub-levels)
    • AMS: 46S10    Functional analysis over fields other than R or C or the quaternions; non-Archimedean functional analysis
    • AMS: 46S20    Nonstandard functional analysis
    • AMS: 46S99    None of the above, but in this section
  • AMS: 46Txx    Nonlinear functional analysis
    AMS: 46T*     (including sub-levels)
    • AMS: 46T12    Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds
    • AMS: 46T20    Continuous and differentiable maps
    • AMS: 46T99    None of the above, but in this section

OPERATOR THEORY

 AMS: 47       All of this section
AMS: 47-XX    Not classified at a more specific level
  • AMS: 47Axx    General theory of linear operators
    AMS: 47A*     (including sub-levels)
    • AMS: 47A05    General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
    • AMS: 47A10    Spectrum, resolvent
    • AMS: 47A15    Invariant subspaces
    • AMS: 47A16    Cyclic and hypercyclic vectors
    • AMS: 47A20    Dilations, extensions, compressions
    • AMS: 47A25    Spectral sets
    • AMS: 47A30    Norms (inequalities, more than one norm, etc.)
    • AMS: 47A35    Ergodic theory
    • AMS: 47A40    Scattering theory
    • AMS: 47A48    Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.
    • AMS: 47A53    (Semi-) Fredholm operators; index theories
    • AMS: 47A55    Perturbation theory
    • AMS: 47A56    Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)
    • AMS: 47A58    Operator approximation theory
    • AMS: 47A60    Functional calculus
    • AMS: 47A64    Operator means, shorted operators, etc.
    • AMS: 47A65    Structure theory
    • AMS: 47A67    Representation theory
    • AMS: 47A68    Factorization theory (including Wiener-Hopf and spectral factorizations)
    • AMS: 47A70    (Generalized) eigenfunction expansions; rigged Hilbert spaces
    • AMS: 47A75    Eigenvalue problems
    • AMS: 47A80    Tensor products of operators
    • AMS: 47A99    None of the above, but in this section
  • AMS: 47Bxx    Special classes of linear operators
    AMS: 47B*     (including sub-levels)
    • AMS: 47B06    Riesz operators; eigenvalue distributions; approximation numbers, $s$-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
    • AMS: 47B10    Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.)
    • AMS: 47B15    Hermitian and normal operators (spectral measures, functional calculus, etc.)
    • AMS: 47B20    Subnormal operators, hyponormal operators, etc.
    • AMS: 47B25    Symmetric and selfadjoint operators (unbounded)
    • AMS: 47B32    Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)
    • AMS: 47B33    Composition operators
    • AMS: 47B34    Kernel operators
    • AMS: 47B35    Toeplitz operators, Hankel operators, Wiener-Hopf operators
    • AMS: 47B37    Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
    • AMS: 47B38    Operators on function spaces (general)
    • AMS: 47B39    Difference operators
    • AMS: 47B40    Spectral operators, decomposable operators, well-bounded operators, etc.
    • AMS: 47B47    Commutators, derivations, elementary operators, etc.
    • AMS: 47B48    Operators on Banach algebras
    • AMS: 47B49    Transformers (= operators on spaces of operators)
    • AMS: 47B60    Operators on ordered spaces
    • AMS: 47B65    Positive operators and order-bounded operators
    • AMS: 47B80    Random operators
    • AMS: 47B99    None of the above, but in this section
  • AMS: 47Cxx    Individual linear operators as elements of algebraic systems
    AMS: 47C*     (including sub-levels)
  • AMS: 47Dxx    Groups and semigroups of linear operators, their generalizations and applications
    AMS: 47D*     (including sub-levels)
    • AMS: 47D03    Groups and semigroups of linear operators
    • AMS: 47D06    One-parameter semigroups and linear evolution equations
    • AMS: 47D07    Markov semigroups and applications to diffusion processes
    • AMS: 47D08    Schrödinger and Feynman-Kac semigroups
    • AMS: 47D09    Operator sine and cosine functions and higher-order Cauchy problems
  • AMS: 47Exx    Ordinary differential operators
    AMS: 47E*     (including sub-levels)
  • AMS: 47Fxx    Partial differential operators
    AMS: 47F*     (including sub-levels)
  • AMS: 47Gxx    Integral, integro-differential, and pseudodifferential operators
    AMS: 47G*     (including sub-levels)
  • AMS: 47Hxx    Nonlinear operators and their properties
    AMS: 47H*     (including sub-levels)
    • AMS: 47H04    Set-valued operators
    • AMS: 47H05    Monotone operators (with respect to duality)
    • AMS: 47H07    Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
    • AMS: 47H10    Fixed-point theorems
    • AMS: 47H11    Degree theory
    • AMS: 47h20    Semigroups of nonlinear operators
    • AMS: 47h20    Particular nonlinear operators (superposition, Hammerstein, Nemytskii, Uryson, etc.)
    • AMS: 47H40    Random operators
  • AMS: 47Jxx    Equations and inequalities involving nonlinear operators
    AMS: 47J*     (including sub-levels)
    • AMS: 47J05    Equations involving nonlinear operators (general)
    • AMS: 47J10    Nonlinear eigenvalue problems
    • AMS: 47J15    Abstract bifurcation theory
    • AMS: 47J20    Variational and other types of inequalities involving nonlinear operators (general)
    • AMS: 47J25    Methods for solving nonlinear operator equations (general)
    • AMS: 47J35    Nonlinear evolution equations
  • AMS: 47Lxx    Linear spaces and algebras of operators
    AMS: 47L*     (including sub-levels)
    • AMS: 47L05    Linear spaces of operators
    • AMS: 47L10    Algebras of operators on Banach spaces and other topological linear spaces
    • AMS: 47L15    Operator algebras with symbol structure
    • AMS: 47L25    Operator spaces (=matricially normed spaces)
    • AMS: 47L30    Abstract operator algebras on Hilbert spaces
    • AMS: 47L55    Representations of (nonselfadjoint) operator algebras
    • AMS: 47L60    Algebras of unbounded operators; partial algebras of operators
    • AMS: 47L80    Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)
    • AMS: 47L90    Applications of operator algebras to physics
  • AMS: 47Nxx    Miscellaneous applications of operator theory
    AMS: 47N*     (including sub-levels)
    • AMS: 47N10    Applications in optimization, convex analysis, mathematical programming, economics
    • AMS: 47N20    Applications to differential and integral equations
    • AMS: 47N40    Applications in numerical analysis
    • AMS: 47N50    Applications in quantum physics
    • AMS: 47N60    Applications in biology and other sciences
    • AMS: 47N70    Applications in systems theory, circuits, etc.
  • AMS: 47Sxx    Other (nonclassical) types of operator theory
    AMS: 47S*     (including sub-levels)
    • AMS: 47S10    Operator theory over fields other than R, C or the quaternions; non-Archimedean operator theory
    • AMS: 47S20    Nonstandard operator theory

CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION

 AMS: 49       All of this section
AMS: 49-XX    Not classified at a more specific level Letzte Änderung: 20.07.2012 Gabriele Dörflinger
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