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47: Operator theory


Introduction

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.

History

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.

Applications and related fields

[Schematic of subareas and related areas]

Subfields

Browse all (old) classifications for this area at the AMS.


Textbooks, reference works, and tutorials

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

Software and tables

Other web sites with this focus

Selected topics at this site


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