Functional Calculi.
Başlık:
Functional Calculi.
Yazar:
Swartz, Charles.
ISBN:
9789814415989
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 online resource (228 pages)
İçerik:
Contents -- Preface -- 1. Vector and Operator Valued Measures -- 1.1 Vector Measures -- 1.2 Operator Valued Measures -- 1.3 Extensions of Measures -- 1.4 Regularity and Countable Additivity -- 1.5 Countable Additivity on Products -- 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 -- 5.1 Vector Valued Measurable Functions -- 5.2 Integrating Vector Valued Functions -- 6. An Abstract Functional Calculus -- 7. The Riesz Operational Calculus -- 7.1 Power Series -- 7.2 Laurent Series -- 7.3 Runge's Theorem -- 7.4 Several Complex Variables -- 7.5 Riesz Operational Calculus -- 7.6 Abstract Functional Calculus -- 7.7 Spectral Sets -- 7.8 Isolated Points -- 7.9 Wiener's Theorem -- 8. Weyl's Functional Calculus -- Appendix A The Orlicz-Pettis Theorem -- Appendix B The Spectrum of an Operator -- Appendix C Self Adjoint, Normal and Unitary Operators -- Appendix D Sesquilinear Functionals -- Appendix E Tempered Distributions and the Fourier Transform -- E.1 Distributions -- E.2 The Spaces S(Rn) and S'(Rn) -- E.3 Fourier Transform of Functions -- E.4 Fourier Transform of a Tempered Distribution -- E.5 Paley-Wiener Theorems -- Bibliography -- Index.
Özet:
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.
Notlar:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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