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[Texts]## 47: Operator theory |

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.

- 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

- Here are the AMS and Goettingen resource pages for area 47.

- Norms of operators on Hilbert space.
- Recognizing a tensor product of operators on Hilbert spaces
- Heisenberg's Inequality on non-commuting operators
- Parameterizations of unitary operators on a Hilbert space (and thus parameterization of the unitary and orthogonal groups).
- What's beyond Bochner integrals? (Pettis integral, Birkhoff integral)
- The Mean Ergodic Theorem -- average values of iterates of an operator on Hilbert space.

Last modified 2000/01/14 by Dave Rusin. Mail: