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Record Nr. |
UNINA9910786967403321 |
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Autore |
Bosch Carlos |
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Titolo |
Functional calculi / / Carlos Bosch, Instituto Tecnologico Autonomo de Mexico, Mexico, Charles Swartz, New Mexico State University, USA |
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Pubbl/distr/stampa |
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Singapore, : World Scientific, c2013 |
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New Jersey : , : World Scientific, , [2013] |
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�2013 |
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ISBN |
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Descrizione fisica |
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1 online resource (x, 215 pages) : illustrations |
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Collana |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Preface; Contents; 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 Theorem7.4 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 TheoremsBibliography; Index |
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Sommario/riassunto |
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A functional calculus is a construction which associates with an operator or a family of operators a homomorphism from a function |
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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 |
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