03132oam 2200457 450 991081451960332120190911112728.0981-4415-98-7(OCoLC)843872845(MiFhGG)GVRL8RIZ(EXLCZ)99267000000036182920130813h20132013 uy 0engurun|---uuuuatxtccrFunctional calculi /Carlos Bosch, Instituto Tecnologico Autonomo de Mexico, Mexico, Charles Swartz, New Mexico State University, USASingapore World Scientificc2013New Jersey :World Scientific,[2013]�20131 online resource (x, 215 pages) illustrationsGale eBooksDescription based upon print version of record.981-4415-97-9 Includes bibliographical references and index.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 Series7.3 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 DistributionE.5 Paley-Wiener TheoremsBibliography; IndexA 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-adjointFunctional analysisFunctional analysis.515Bosch Carlos136133Swartz Charles1938-MiFhGGMiFhGGBOOK9910814519603321Functional calculi4078905UNINA