Operator theory
著者
書誌事項
Operator theory
（A comprehensive course in analysis, pt. 4）
American Mathematical Society, c2015
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注記
Includes bibliographical references and indexes
内容説明・目次
内容説明
A Comprehensive Course in Analysis by Poincare Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis.
Part 4 focuses on operator theory, especially on a Hilbert space. Central topics are the spectral theorem, the theory of trace class and Fredholm determinants, and the study of unbounded self-adjoint operators. There is also an introduction to the theory of orthogonal polynomials and a long chapter on Banach algebras, including the commutative and non-commutative Gel'fand-Naimark theorems and Fourier analysis on general locally compact abelian groups.
目次
Preliminaries
Operator basics
Compact operators, mainly on a Hilbert space
Orthogonal polynomials
The spectral theorem
Banach algebras
Bonus chapter: Unbounded self-adjoint operators
Bibliography
Symbol index
Subject index
Author index
Index of capsule biographies
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