Operator theory studies transformations between
the vector spaces studied in Functional Analysis, such as differential
operators or self-adjoint operators. The analysis might study the spectrum
of an individual operator or the semigroup structure of a collection of them.
See e.g. Felippa, Carlos A.: "50 year classic reprint: an appreciation of R. Courant's "Variational methods for the solution of problems of equilibrium and vibrations" [Bull. Amer. Math. Soc. 49 (1943), 1--23; MR 4, 200]", Internat. J. Numer. Methods Engrg. 37 (1994), no. 13, 2159--2187.
- 47A: General theory of linear operators
- 47B: Special classes of linear operators
- 47C: Individual linear operators as elements of algebraic systems
- 47D: Groups and semigroups of linear operators, their generalizations and applications. See also 46LXX
- 47E05: Ordinary differential operators, See also 34BXX, 34LXX, 58F19
- 47F05: Partial differential operators, See also 35PXX, 58G05
- 47G: Integral, integro-differential, and pseudodifferential operators
- 47H: Nonlinear operators, For global and geometric aspects, see 58-XX, especially 58CXX
- 47J: Equations and inequalities involving linear operators [new in 2000]
- 47L: Linear spaces and algebras of operators (See also 46Lxx) [new in 2000]
- 47N: Miscellaneous applications of operator theory, see also 46NXX
- 47S: Other (nonclassical) types of operator theory, see also 46SXX
Browse all (old) classifications for this area at the AMS.
Jörgens, Konrad: "Linear integral operators",
Surveys and Reference Works in Mathematics, 7.
Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982. 379 pp. ISBN 0-273-08523-9 MR83j:45001 (German original: MR 57#1036)
There is a journal specializing in this area:
Integral Equations and Operator Theory
"Reviews on Operator Theory, 1980-1986", AMS
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