| 47-XX | | Prev: 46 | Up: Top | Next: 49 | |
| 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
[xref: 35Pxx]
| 47A05 |
General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
| 47A06 |
Linear relations (multivalued linear operators)
| 47A07 |
Forms (bilinear, 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 28Dxx, 37Axx]
[xref: 28Dxx]
| 47A40 |
Scattering theory [See also 34L25, 35P25, 81Uxx]
[xref: 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.
[xref: 93B28]
| 47A50 |
Equations and inequalities involving linear operators, with vector unknowns
[xref: 35R20]
| 47A52 |
Ill-posed problems, regularization
| 47A53 |
(Semi-) Fredholm operators; index theories [See also 58B15, 58J20]
[xref: 58B15]
| 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]
[xref: 93B28]
| 47A58 |
Operator approximation theory
| 47A60 |
Functional calculus
[xref: 46H30]
| 47A62 |
Equations involving linear operators, with operator unknowns
| 47A63 |
Operator inequalities
| 47A64 |
Operator means, shorted operators, etc.
[xref: 26E60]
| 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]
[xref: 45C05, 49R50]
| 47A80 |
Tensor products of operators [See also 46M05]
[xref: 46M05]
| 47A99 |
None of the above, but in this section
| |
47Bxx
| Special classes of linear operators
[xref: 35Pxx]
| 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 (including de Branges, de Branges-Rovnyak, and other structured spaces) [See also 46E22]
[xref: 46E22]
| 47B33 |
Composition operators
| 47B34 |
Kernel operators
| 47B35 |
Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
[xref: 45E10, 93B28]
| 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)
[xref: 45P05]
| 47B39 |
Difference operators [See also 39A70]
[xref: 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]
[xref: 46C20]
| 47B60 |
Operators on ordered spaces
| 47B65 |
Positive operators and order-bounded operators
| 47B80 |
Random operators [See also 60H25]
[xref: 37Hxx, 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
[xref: 34Gxx, 34K30]
| 47D03 |
Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20}
[xref: 20M20, 35R20, 60J35]
| 47D06 |
One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]
[xref: 34G10, 35R20]
| 47D07 |
Markov semigroups and applications to diffusion processes {For Markov processes, see 60Jxx}
[xref: 60J35]
| 47D08 |
Schrödinger and Feynman-Kac semigroups
| 47D09 |
Operator sine and cosine functions and higher-order Cauchy problems [See also 34G10]
[xref: 34G10, 35R20]
| Operator algebras on Hilbert space Operator algebras on Banach spaces and other linear topological spaces Applications of operator algebras to physics 47D60 |
$C$-semigroups
| 47D62 |
Integrated semigroups
| 47D99 |
None of the above, but in this section
| |
47E05
| Ordinary differential operators [See also 34Bxx, 34Lxx]
[xref: 34Lxx]
| |
47F05
| Partial differential operators [See also 35Pxx, 58Jxx]
[xref: 35Pxx]
| |
47Gxx
| Integral, integro-differential, and pseudodifferential operators [See also 58Jxx]
| 47G10 |
Integral operators [See also 45P05]
[xref: 45P05, 47B35]
| 47G20 |
Integro-differential operators [See also 34K30, 35R10, 45J05, 45K05]
[xref: 45J05, 45K05]
| 47G30 |
Pseudodifferential operators [See also 35Sxx, 58Jxx]
[xref: 35Sxx]
| 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}
[xref: 34G20, 34Gxx, 34K30, 46Txx, 58Cxx, 65H17]
| 47H04 |
Set-valued operators [See also 28B20, 54C60, 58C06]
[xref: 49J53, 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 [Sse also 54H25, 55M20, 58C30]
[xref: 26A18, 54H25, 58C30]
| 47H11 |
Degree theory [See also 55M25, 58C30]
| 47H14 |
Perturbations of nonlinear operators
| 47H20 |
Semigroups of nonlinear operators
[xref: 20M20, 35R20, 58D07]
| 47H30 |
Particular nonlinear operators (superposition, Hammerstein, Nemytskii, Uryson, etc.) [See also 45Gxx, 45P05]
[xref: 45Gxx]
| 47H40 |
Random operators [See also 60H25]
| 47H50 |
Potential operators
| 47H60 |
Multilinear and polynomial operators [See also 46G25]
[xref: 46E50, 46G25]
| 47H99 |
None of the above, but in this section
| |
47Jxx
| Equations and inequalities involving nonlinear operators [See also 46Txx] {For global and geometric aspects, see 58-XX}
[xref: 34G20, 34Gxx, 35R20, 39B42, 45Gxx, 46Txx, 58Cxx, 58D25, 65H17]
| 47J05 |
Equations involving nonlinear operators (general)
| 47J06 |
Nonlinear ill-posed problems
| 47J07 |
Abstract inverse mapping and implicit function theorems [See also 46T20 and 58C15]
| 47J10 |
Nonlinear eigenvalue problems
[xref: 58C40]
| 47J15 |
Abstract bifurcation theory [See also 58E07, 58E09]
| 47J20 |
Variational and other types of inequalities involving nonlinear operators (general)
| 47J25 |
Methods for solving nonlinear operator equations (general)
| 47J30 |
Variational methods [See also 58Exx]
| 47J35 |
Nonlinear evolution equations [See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 58D25]
| 47J40 |
Equations with hysteresis operators
| 47J99 |
None of the above, but in this section
| |
47Lxx
| Linear spaces and algebras of operators [See also 46Lxx]
[xref: 46H35, 46Lxx]
| 47L05 |
Linear spaces of operators [See also 46A32 and 46B28]
[xref: 46A32, 46B28]
| 47L07 |
Convex sets and cones of operators [See also 46A55]
| 47L10 |
Algebras of operators on Banach spaces and other topological linear spaces
| 47L15 |
Operator algebras with symbol structure
| 47L20 |
Operator ideals
[xref: 46A32, 46B28, 47B10]
| 47L25 |
Operator spaces (=matricially normed spaces) [See also 46L07]
[xref: 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
[xref: 46L60]
| 47L99 |
None of the above, but in this section
| |
47Nxx
| Miscellaneous applications of operator theory [See also 46Nxx]
[xref: 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.
[xref: 93B28]
| 47N99 |
None of the above, but in this section
| |
47Sxx
| Other (nonclassical) types of operator theory [See also 46Sxx]
[xref: 46Sxx]
| 47S10 |
Operator theory over fields other than R, C or the quaternions; non-Archimedean operator theory
[xref: 12J25, 12J27]
| 47S20 |
Nonstandard operator theory [See also 03H05]
[xref: 03H05]
| 47S30 |
Constructive operator theory [See also 03F60]
[xref: 03F60]
| 47S40 |
Fuzzy operator theory [See also 03E72]
| 47S50 |
Operator theory in probabilistic metric linear spaces
| 47S99 |
None of the above, but in this section
| |