|
47-XX
|
Operator theory
|
|
47-00
|
General reference works (handbooks, dictionaries, bibliographies, etc.)
|
|
47-01
|
Instructional exposition (textbooks, tutorial papers, etc.)
|
|
47-02
|
Research exposition (monographs, survey articles)
|
|
47-03
|
Historical {!must also be assigned at least one classification number from section 01}
|
|
47-04
|
Explicit machine computation and programs (not the theory of computation or programming)
|
|
47-06
|
Proceedings, conferences, collections, etc.
|
|
47Axx
|
General theory of linear operators
|
|
47A05
|
General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
|
|
47A06
|
Linear relations (multivalued linear operators)
|
|
47A07
|
Forms (blilinear, sesquilinear, multilinear)
|
|
47A10
|
Spectrum, resolvent
|
|
47A11
|
Local spectral properties
|
|
47A12
|
Numerical range, numerical radius
|
|
47A13
|
Several-variable operator theory (spectral, Fredholm, etc.)
|
|
47A15
|
Invariant subspaces
|
|
47A16
|
Cyclic and hypercyclic vectors
|
|
47A20
|
Dilations, extensions, compressions
|
|
47A25
|
Spectral sets
|
|
47A30
|
Norms (inequalities, more than one norm, etc.)
|
|
47A35
|
Ergodic theory
[See also
37Axx]
|
|
47A40
|
Scattering theory
[See also
34L25,
35P25,
81Uxx]
|
|
47A45
|
Canonical models for contractions and nonselfadjoint operators
|
|
47A46
|
Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.
|
|
47A48
|
Operator colligations (=nodes), vessels, linear systems, characteristic functions, realizations, etc.
|
|
47A50
|
Equations and inequalities involving linear operators, with vector unknowns
|
|
47A53
|
(Semi-) Fredholm operators; index theories
[See also
58B10,
58J20]
|
|
47A55
|
Perturbation theory
|
|
47A56
|
Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)
|
|
47A57
|
Operator methods in interpolation, moment and extension problems
[See also
30E05,
42A70,
42A82,
44A60]
|
|
47A58
|
Operator approximation theory
|
|
47A60
|
Functional calculus
|
|
47A62
|
Equations involving linear operators, with operator unknowns
|
|
47A63
|
Operator inequalities
|
|
47A64
|
Operator means, shorted operators, etc.
|
|
47A65
|
Structure theory
|
|
47A66
|
Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operators
|
|
47A67
|
Representation theory
|
|
47A68
|
Factorization theory (including Wiener - Hopf and spectral factorizations)
|
|
47A70
|
(Generalized) eigenfunction expansions; rigged Hilbert spaces
|
|
47A75
|
Eigenvalue problems
[See also
49R50]
|
|
47A80
|
Tensor products of operators
[See also
46M05]
|
|
47A99
|
None of the above, but in this section
|
|
47Bxx
|
Special classes of linear operators
|
|
47B06
|
Riesz operators; eigenvalue distributions; approximation numbers, s-numbers, Kolmogorov numbers, entropy numbers, etc.
Of operators
|
|
47B07
|
Operators defined by compactness properties
|
|
47B10
|
Operators belonging to operator ideals (nuclear, p-summing, in the Schatten - von_Neumann classes, etc.)
[See also
47L20]
|
|
47B15
|
Hermitian and normal operators (spectral measures, functional calculus, etc.)
|
|
47B20
|
Subnormal operators, hyponormal operators, etc.
|
|
47B25
|
Symmetric and selfadjoint operators (unbounded)
|
|
47B32
|
Operators in reproducing-kernel Hilbert spaces
|
|
47B33
|
Composition operators
|
|
47B34
|
Kernel operators
|
|
47B35
|
Toeplitz operators, Hankel operators, Wiener - Hopf operators
{For other integral operators, see also
45P05,
47G10}
[See also
32A25,
32M15]
|
|
47B36
|
Jacobi (tridiagonal) operators (matrices) and generalizations
|
|
47B37
|
Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
|
|
47B38
|
Operators on function spaces (general)
|
|
47B39
|
Difference operators
[See also
39A70]
|
|
47B40
|
Spectral operators, decomposable operators, well-bounded operators, etc.
|
|
47B44
|
Accretive operators, dissipative operators, etc.
|
|
47B47
|
Commutators, derivations, elementary operators, etc.
|
|
47B48
|
Operators on Banach algebras
|
|
47B49
|
Transformers (=operators on spaces of operators)
|
|
47B50
|
Operators on spaces with an indefinite metric
[See also
46C50]
|
|
47B60
|
Operators on ordered spaces
|
|
47B65
|
Positive operators and order-bounded operators
|
|
47B80
|
Random operators
[See also
60H25]
|
|
47B99
|
None of the above, but in this section
|
|
47Cxx
|
Individual linear operators as elements of algebraic systems
|
|
47C05
|
Operators in algebras
|
|
47C10
|
Operators in *-algebras
|
|
47C15
|
Operators in C*- or von_Neumann algebras
|
|
47C99
|
None of the above, but in this section
|
|
47Dxx
|
Groups and semigroups of linear operators, their generalizations and applications
|
|
47D03
|
Groups and semigroups of linear operators
{For nonlinear operators, see
47H20}
[See also
20M20]
|
|
47D06
|
One-parameter semigroups and linear evolution equations
[See also
34G10,
34K30]
|
|
47D07
|
Markov semigroups and applications to diffusion processes
{For Markov processes, see
60Jxx}
|
|
47D08
|
Schr\"odinger and Feynman - Kac semigroups
|
|
47D09
|
Operator sine and cosine functions and higher-order Cauchy problems
[See also
34G10]
|
|
47D60
|
C-semigroups
|
|
47D62
|
Integrated semigroups
|
|
47D99
|
None of the above, but in this section
|
|
47E05
|
Ordinary differential operators
[See also
34Bxx,
34Lxx]
|
|
47F05
|
Partial differential operators
[See also
35Pxx,
58Jxx]
|
|
47Gxx
|
Integral, integro-differential, and pseudodifferential operators
[See also
58Jxx]
|
|
47G10
|
Integral operators
[See also
45P05]
|
|
47G20
|
Integro-differential operators
[See also
34K30,
35R10,
45J05,
45K05]
|
|
47G30
|
Pseudodifferential operators
[See also
35Sxx,
58Jxx]
|
|
47G99
|
None of the above, but in this section
|
|
47Hxx
|
Nonlinear operators and their properties
{For global and geometric aspects, see
58-XX,
especially
58Cxx}
|
|
47H04
|
Set-valued operators
[See also
28B20,
54C60,
58C06]
|
|
47H05
|
Monotone operators (with respect to duality)
|
|
47H06
|
Accretive operators, dissipative operators, etc.
|
|
47H07
|
Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
|
|
47H09
|
Nonexpansive mappings, and their generalizations (ultimately compact mappings, measures of noncompactness and condensing mappings, A-proper mappings, K-set contractions, etc.)
|
|
47H10
|
Fixed-point theorems
[See also
54H25,
55M20,
58C30]
|
|
47H11
|
Degree theory
[See also
55M25,
58C30]
|
|
47H12
|
Spectral theory of nonlinear operators
[See also
58C40]
|
|
47H14
|
Perturbations of nonlinear operators
|
|
47H20
|
Semigroups of nonlinear operators
|
|
47H30
|
Particular nonlinear operators (superposition, Hammerstein, Nemytski\u\i, Uryson, etc.)
[See also
45P05]
|
|
47H40
|
Random operators
[See also
60H25]
|
|
47H50
|
Potential operators
|
|
47H60
|
Multilinear and polynomial operators
[See also
46G25]
|
|
47H99
|
None of the above, but in this section
|
|
47Jxx
|
Equations and inequalities involving linear operators
|
|
47J05
|
Equations involving nonlinear operators (general)
|
|
47J07
|
Abstract inverse mapping and implicit function theorems
[See also
46T20
and
58C15]
|
|
47J10
|
Nonlinear eigenvalue problems
|
|
47J15
|
Abstract bifurcation theory
[See also
58E07,
58E09]
|
|
47J20
|
Variational and other type of inequalities involving nonlinear operators (general)
|
|
47J25
|
Methods for solving nonlinear operator equations (general)
|
|
47J30
|
Infinite-dimensional critical point theory and variational methods
[See also
58Exx]
|
|
47J35
|
Nonlinear evolution equations
[See also
34G20,
35K90,
35L90,
35Qxx,
35R20,
47H20,
58D25]
|
|
47J40
|
Equations with hysteresis
|
|
47J99
|
None of the above, but in this section
|
|
47Lxx
|
Linear spaces and algebras of operators
[See also
46Lxx]
|
|
47L05
|
Linear spaces of operators
[See also
46A32
and
46B28]
|
|
47L07
|
Convex sets and cones of operators
[See also
46A55,
90C25,
and
90C31]
|
|
47L10
|
Algebras of operators on Banach spaces and other topological linear spaces
|
|
47L15
|
Operator algebras with symbol structure
|
|
47L20
|
Operator ideals
|
|
47L25
|
Operator spaces (=matricially normed spaces)
[See also
46L07]
|
|
47L30
|
Abstract operator algebras on Hilbert spaces
|
|
47L35
|
Nest algebras, CSL algebras
|
|
47L40
|
Limit algebras, subalgebras of C*-algebras
|
|
47L45
|
Dual algebras; weakly closed singly generated operator algebras
|
|
47L50
|
Dual spaces of operator algebras
|
|
47L55
|
Representations of (nonselfadjoint) operator algebras
|
|
47L60
|
Algebras of unbounded operators; partial algebras of operators
|
|
47L65
|
Crossed product algebras (analytic crossed products)
|
|
47L70
|
Nonassociative nonselfadjoint operator algebras
|
|
47L75
|
Other nonselfadjoint operator algebras
|
|
47L80
|
Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)
|
|
47L90
|
Applications of operator algebras to physics
|
|
47L99
|
None of the above, but in this section
|
|
47Nxx
|
Miscellaneous applications of operator theory
[See also
46Nxx]
|
|
47N10
|
Applications in optimization, convex analysis, mathematical programming, economics
|
|
47N20
|
Applications to differential and integral equations
|
|
47N30
|
Applications in probability theory and statistics
|
|
47N40
|
Applications in numerical analysis
[See also
65Jxx]
|
|
47N50
|
Applications in quantum physics
|
|
47N55
|
Applications in statistical physics
|
|
47N60
|
Applications in biology and other sciences
|
|
47N70
|
Applications in systems theory, circuits, etc.
|
|
47N99
|
None of the above, but in this section
|
|
47Sxx
|
Other (nonclassical) types of operator theory
[See also
46Sxx]
|
|
47S10
|
Operator theory over fields other than R, C or the quaternions; non-Archimedean operator theory
|
|
47S20
|
Nonstandard operator theory
[See also
03H05]
|
|
47S30
|
Constructive operator theory
[See also
03F65]
|
|
47S40
|
Fuzzy operator theory
[See also
03E72]
|
|
47S50
|
Operator theory in probabilistic metric linear spaces
|
|
47S99
|
None of the above, but in this section
|