46-XX
|
Functional analysis
{For manifolds modeled on topological linear spaces, see
57N20,
58Bxx}
|
46-00
|
General reference works (handbooks, dictionaries, bibliographies, etc.)
|
46-01
|
Instructional exposition (textbooks, tutorial papers, etc.)
|
46-02
|
Research exposition (monographs, survey articles)
|
46-03
|
Historical {!must also be assigned at least one classification number from section 01}
|
46-04
|
Explicit machine computation and programs (not the theory of computation or programming)
|
46-06
|
Proceedings, conferences, collections, etc.
|
46Axx
|
Topological linear spaces and related structures
{For function spaces, see
46Exx}
|
46A03
|
General theory of locally convex spaces
|
46A04
|
Locally convex Fr\'echet spaces and (DF)-spaces
|
46A08
|
Barrelled spaces, bornological spaces
|
46A11
|
Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
|
46A13
|
Spaces defined by inductive or projective limits (LB, LF, etc.)
[See also
46M40]
|
46A16
|
Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
|
46A17
|
Bornologies and related structures; Mackey convergence, etc.
|
46A19
|
Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \bfR, etc.)
|
46A20
|
Duality theory
|
46A22
|
Theorems of Hahn - Banach type; extension and lifting of functionals and operators
[See also
46M10]
|
46A25
|
Reflexivity and semi-reflexivity
[See also
46B10]
|
46A30
|
Open mapping and closed graph theorems; completeness (including B-, Br-completeness)
|
46A32
|
Spaces of linear operators; topological tensor products; approximation properties
[See also
46B28,
46M05,
47L05,
47L20]
|
46A35
|
Summability and bases
[See also
46B15]
|
46A40
|
Ordered topological linear spaces, vector lattices
[See also
06F20,
46B40,
46B42]
|
46A45
|
Sequence spaces (including K\"othe sequence spaces)
[See also
46B45]
|
46A50
|
Compactness in topological linear spaces; angelic spaces, etc.
|
46A55
|
Convex sets in topological linear spaces; Choquet theory
[See also
52A07]
|
46A61
|
Graded Fr\'echet spaces and tame operators
|
46A63
|
Topological invariants ((DN), (\Omega), etc.)
|
46A70
|
Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
|
46A80
|
Modular spaces
|
46A99
|
None of the above, but in this section
|
46Bxx
|
Normed linear spaces and Banach spaces; Banach lattices
{For function spaces, see
46Exx}
|
46B03
|
Isomorphic theory (including renorming) of Banach spaces
|
46B04
|
Isometric theory of Banach spaces
|
46B07
|
Local theory of Banach spaces
|
46B08
|
Ultraproduct techniques in Banach space theory
[See also
46M07]
|
46B09
|
Probabilistic methods in Banach space theory
[See also
60Bxx]
|
46B10
|
Duality and reflexivity
[See also
46A25]
|
46B15
|
Summability and bases
[See also
46A35]
|
46B20
|
Geometry and structure of normed linear spaces
|
46B22
|
Radon - Nikodym, Kreuin - Milman and related properties
[See also
46G10]
|
46B25
|
Classical Banach spaces in the general theory
|
46B26
|
Nonseparable Banach spaces
|
46B28
|
Spaces of operators; tensor products; approximation properties
[See also
46A32,
46M05,
47L05,
47L20]
|
46B40
|
Ordered normed spaces
[See also
46A40,
46B42]
|
46B42
|
Banach lattices
[See also
46A40,
46B40]
|
46B45
|
Banach sequence spaces
[See also
46A45]
|
46B50
|
Compactness in Banach (or normed) spaces
|
46B70
|
Interpolation between normed linear spaces
[See also
46M35]
|
46B99
|
None of the above, but in this section
|
46Cxx
|
Inner product spaces and their generalizations, Hilbert spaces
{For function spaces, see
46Exx}
|
46C05
|
Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
|
46C07
|
Hilbert subspaces; complementation (Aronszajn, de_Branges, ...)
[See
46B70,
46M35]
|
46C15
|
Characterizations of Hilbert spaces
|
46C20
|
Spaces with indefinite inner product (Krein spaces, Pontryagin spaces, ...)
|
46C50
|
Generalizations of inner products (semi-inner products, partial inner products, etc.)
|
46C99
|
None of the above, but in this section
|
46Exx
|
Linear function spaces and their duals
[See also
30H05,
32A38,
46F05]
{For function algebras, see
46J10}
|
46E05
|
Lattices of continuous, differentiable or analytic functions
|
46E10
|
Topological linear spaces of continuous, differentiable or analytic functions
|
46E15
|
Banach spaces of continuous, differentiable or analytic functions
|
46E20
|
Hilbert spaces of continuous, differentiable or analytic functions
|
46E22
|
Hilbert spaces with reproducing kernels (=
[Proper] functional Hilbert spaces)
|
46E25
|
Rings and algebras of continuous, differentiable or analytic functions
{For Banach function algebras, see
46J10,
46J15}
|
46E27
|
Spaces of measures
[See also
28A33,
46Gxx]
|
46E30
|
Spaces of measurable functions (Lp-spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
|
46E35
|
Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
|
46E39
|
Sobolev (and similar kinds of) spaces of functions of discrete variables
|
46E40
|
Spaces of vector- and operator-valued functions
|
46E50
|
Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
[See also
46G20,
46G25,
47H60]
|
46E99
|
None of the above, but in this section
|
46Fxx
|
Distributions, generalized functions, distribution spaces
[See also
46T30]
|
46F05
|
Topological linear spaces of test functions, distributions and ultradistributions
[See also
46E10,
46E35]
|
46F10
|
Operations with distributions
|
46F12
|
Integral transforms in distribution spaces
[See also
42-XX,
44-XX]
|
46F15
|
Hyperfunctions, analytic functionals
[See also
32A25,
32A45,
32C35,
58J15]
|
46F20
|
Distributions and ultradistributions as boundary values of analytic functions
[See also
30D40,
30E25,
32A40]
|
46F25
|
Distributions on infinite-dimensional spaces
[See also
58C35]
|
46F30
|
Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
|
46F99
|
None of the above, but in this section
|
46Gxx
|
Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
[See also
28-XX,
46Txx]
|
46G05
|
Derivatives
[See also
46T20,
58C20,
58C25]
|
46G10
|
Vector-valued measures and integration
[See also
28Bxx,
46B22]
|
46G12
|
Measures and integration on abstract linear spaces
[See also
28C20,
46T12]
|
46G15
|
Functional analytic lifting theory
[See also
28A51]
|
46G20
|
Infinite-dimensional holomorphy
[See also
32-XX,
46E50,
46T25
58B12,
58C10]
|
46G25
|
(Spaces of) multilinear mappings, polynomials
[See also
46E50,
46G20,
47H60]
|
46G99
|
None of the above, but in this section
|
46Hxx
|
Topological algebras, normed rings and algebras, Banach algebras
{For group algebras, convolution algebras and measure algebras, see
43A10,
43A20}
|
46H05
|
General theory of topological algebras
|
46H10
|
Ideals and subalgebras
|
46H15
|
Representations of topological algebras
|
46H20
|
Structure, classification of topological algebras
|
46H25
|
Normed modules and Banach modules, topological modules {!if not placed in
13-XX
or
16-XX}
|
46H30
|
Functional calculus in topological algebras
[See also
47A60]
|
46H35
|
Topological algebras of operators
[See mainly
47Lxx]
|
46H40
|
Automatic continuity
|
46H70
|
Nonassociative topological algebras
[See also
46K70,
46L70]
|
46H99
|
None of the above, but in this section
|
46Jxx
|
Commutative Banach algebras and commutative topological algebras
[See also
46E25]
|
46J05
|
General theory of commutative topological algebras
|
46J10
|
Banach algebras of continuous functions, function algebras
[See also
46E25]
|
46J15
|
Banach algebras of differentiable or analytic functions, Hp-spaces
[See also
30D55,
30H05,
32A35,
32A37,
32A38,
42B30]
|
46J20
|
Ideals, maximal ideals, boundaries
|
46J25
|
Representations of commutative topological algebras
|
46J30
|
Subalgebras
|
46J40
|
Structure, classification of commutative topological algebras
|
46J45
|
Radical Banach algebras
|
46J99
|
None of the above, but in this section
|
46Kxx
|
Topological (rings and) algebras with an involution
[See also
16W10]
|
46K05
|
General theory of topological algebras with involution
|
46K10
|
Representations of topological algebras with involution
|
46K15
|
Hilbert algebras
|
46K50
|
Nonselfadjoint (sub)algebras in algebras with involution
|
46K70
|
Nonassociative topological algebras with an involution
[See also
46H70,
46L70]
|
46K99
|
None of the above, but in this section
|
46Lxx
|
Selfadjoint operator algebras (C*-algebras, von_Neumann (W*-) algebras, etc.)
[See also
22D25]
|
46L05
|
General theory of C*-algebras
|
46L06
|
Tensor products of C*-algebras; free products of C*-algebras
|
46L07
|
Operator spaces and completely bounded map
[See also
47L25]
|
46L08
|
C*-modules
|
46L10
|
General theory of von_Neumann algebras
|
46L30
|
States
|
46L35
|
Classifications of C*-algebras, factors
|
46L37
|
Subfactors and their classification
|
46L40
|
Automorphisms
|
46L45
|
Decomposition theory for C*-algebras
|
46L51
|
Noncommutative measure and integration
|
46L52
|
Noncommutative function spaces
|
46L53
|
Noncommutative probability and statistics
|
46L54
|
Free probability and free operator algebras
|
46L55
|
Noncommutative dynamical systems
[See also
28Dxx,
54H20,
37Kxx,
37Lxx]
|
46L57
|
Derivations, dissipations and positive semigroups in C*-algebras
|
46L60
|
Applications of selfadjoint operator algebras to physics
[See also
46N50,
46N55,
47L90,
81T05,
82B10,
82C10]
|
46L65
|
Quantizations, deformations
|
46L70
|
Nonassociative selfadjoint operator algebras
[See also
46H70,
46K70]
|
46L80
|
K-theory and operator algebras (including cyclic theory)
[See also
18F25,
19Kxx,
46M20,
55Rxx,
58J22]
|
46L85
|
Noncommutative topology
[See also
58B32,
58B34,
58J22]
|
46L87
|
Noncommutative differential geometry
[See also
58B32,
58B34,
58J22]
|
46L89
|
Other ``noncommutative'' mathematics based on C*-algebra theory
[See also
58B32,
58B34,
58J22]
|
46L99
|
None of the above, but in this section
|
46Mxx
|
Methods of category theory in functional analysis
[See also
18-XX]
|
46M05
|
Tensor products
[See also
46A32,
46B28,
47A80]
|
46M07
|
Ultraproducts
[See also
46B08,
46S20]
|
46M10
|
Projective and injective objects
[See also
46A22]
|
46M15
|
Categories, functors
{For K-theory, EXT, etc., see
19K33,
46L80,
46M18,
46M20}
|
46M18
|
Homological methods (exact sequences, right inverses, lifting, etc.,)
|
46M20
|
Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
[See also
14F05,
18Fxx,
19Kxx,
32Cxx,
32Lxx,
46L80,
46M15,
46M18,
55Rxx]
|
46M35
|
Abstract interpolation of topological vector spaces
[See also
46B70]
|
46M40
|
Inductive and projective limits
[See also
46A13]
|
46M99
|
None of the above, but in this section
|
46Nxx
|
Miscellaneous applications of functional analysis
[See also
47Nxx]
|
46N10
|
Applications in optimization, convex analysis, mathematical programming, economics
|
46N20
|
Applications to differential and integral equations
|
46N30
|
Applications in probability theory and statistics
|
46N40
|
Applications in numerical analysis
[See also
65Jxx]
|
46N50
|
Applications in quantum physics
|
46N55
|
Applications in statistical physics
|
46N60
|
Applications in biology and other sciences
|
46N99
|
None of the above, but in this section
|
46Sxx
|
Other (nonclassical) types of functional analysis
[See also
47Sxx]
|
46S10
|
Functional analysis over fields other than R or C or the quaternions; non-Archimedean functional analysis
[See also
12J25,
32P05]
|
46S20
|
Nonstandard functional analysis
[See also
03H05]
|
46S30
|
Constructive functional analysis
[See also
03F60]
|
46S40
|
Fuzzy functional analysis
[See also
03E72]
|
46S50
|
Functional analysis in probabilistic metric linear spaces
|
46S60
|
Functional analysis on superspaces (supermanifolds) or graded spaces
[See also
58A50
and
58C50]
|
46S99
|
None of the above, but in this section
|
46Txx
|
Nonlinear functional analysis
[See also
47Hxx,
47Jxx,
58Cxx,
58Dxx]
|
46T05
|
Infinite-dimensional manifolds
[See also
53Axx,
58Bxx,
58Dxx,
57N20]
|
46T10
|
Manifolds of mappings
|
46T12
|
Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds
[See also
28Cxx,
46G12,
60-XX]
|
46T20
|
Continuous and differentiable maps
[See also
46G05]
|
46T25
|
Holomorphic maps
[See also
46G20]
|
46T30
|
Distribution and generalized functions on nonlinear spaces
[See also
46Fxx]
|
46T99
|
None of the above, but in this section
|