A primer on Hilbert space operators
著者
書誌事項
A primer on Hilbert space operators
（Compact textbooks in mathematics）
Birkhäuser , Springer, c2018
- : pbk
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注記
Includes bibliographical references (p. 195) and indexes
内容説明・目次
内容説明
The book concisely presents the fundamental aspects of the theory of operators on Hilbert spaces. The topics covered include functional calculus and spectral theorems, compact operators, trace class and Hilbert-Schmidt operators, self-adjoint extensions of symmetric operators, and one-parameter groups of operators.
The exposition of the material on unbounded operators is based on a novel tool, called the z-transform, which provides a way to encode full information about unbounded operators in bounded ones, hence making many technical aspects of the theory less involved.
目次
Spectrum of an operator.- Continuous functional calculus.- Positive operators.- Spectral theorems and functional calculus.- Compact operators.- The trace.- Functional calculus for families of operators.- Operators and their graphs.- z-transform.- Spectral theorems.- Self-adjoint extensions of symmetric operators.- One-parameter groups of unitary operators.- Appendices.- Index of notation.- References - Index.
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