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Functional calculi / Carlos Bosch and Charles Swartz.

By: Contributor(s): Material type: TextTextPublication details: Singapore : World Scientific, c2013.Description: x, 215 p. ; 24 cmISBN:
  • 9789814415972
Subject(s): DDC classification:
  • 23 B742 515.7
Contents:
1. Vector and operator valued measures -- 2. Functions of a self adjoint operator -- 3. Functions of several commuting self adjoint operators -- 4. The spectral theorem for normal operators -- 5. Integrating vector valued functions -- 6. An abstract functional calculus -- 7. The Riesz operational calculus -- 8. Weyl's functional calculus -- Appendix A-- Appendix B-- Appendix C-- Appendix D-- Appendix E-- Bibliography-- index
Summary: A functional calculus is a construction which associates with an operator or a family of operators a homomorphism from a function space into a subspace of continuous linear operators, i.e. a method for defining "functions of an operator". Perhaps the most familiar example is based on the spectral theorem for bounded self-adjoint operators on a complex Hilbert space. This book contains an exposition of several such functional calculi. In particular, there is an exposition based on the spectral theorem for bounded, self-adjoint operators, an extension to the case of several commuting self-adjoint operators and an extension to normal operators. The Riesz operational calculus based on the Cauchy integral theorem from complex analysis is also described. Finally, an exposition of a functional calculus due to H. Weyl is given --
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Includes bibliographical references (pages 209-211) and index.

1. Vector and operator valued measures --
2. Functions of a self adjoint operator --
3. Functions of several commuting self adjoint operators --
4. The spectral theorem for normal operators --
5. Integrating vector valued functions --
6. An abstract functional calculus --
7. The Riesz operational calculus --
8. Weyl's functional calculus --

Appendix A--
Appendix B--
Appendix C--
Appendix D--
Appendix E--

Bibliography--
index

A functional calculus is a construction which associates with an operator or a family of operators a homomorphism from a function space into a subspace of continuous linear operators, i.e. a method for defining "functions of an operator". Perhaps the most familiar example is based on the spectral theorem for bounded self-adjoint operators on a complex Hilbert space. This book contains an exposition of several such functional calculi. In particular, there is an exposition based on the spectral theorem for bounded, self-adjoint operators, an extension to the case of several commuting self-adjoint operators and an extension to normal operators. The Riesz operational calculus based on the Cauchy integral theorem from complex analysis is also described. Finally, an exposition of a functional calculus due to H. Weyl is given --

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