LEADER 03467nam 2200613Ia 450 001 9910462800503321 005 20200520144314.0 010 $a981-4415-98-7 035 $a(CKB)2670000000361829 035 $a(EBL)1193621 035 $a(SSID)ssj0000907108 035 $a(PQKBManifestationID)11553708 035 $a(PQKBTitleCode)TC0000907108 035 $a(PQKBWorkID)10883644 035 $a(PQKB)11735919 035 $a(MiAaPQ)EBC1193621 035 $a(WSP)00003010 035 $a(PPN)189428287 035 $a(Au-PeEL)EBL1193621 035 $a(CaPaEBR)ebr10700503 035 $a(CaONFJC)MIL486893 035 $a(OCoLC)843872845 035 $a(EXLCZ)992670000000361829 100 $a19950605d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFunctional calculi$b[electronic resource] /$fCarlos Bosch and Charles Swartz 210 $aSingapore $cWorld Scientific$dc2013 215 $a1 online resource (228 p.) 300 $aDescription based upon print version of record. 311 $a981-4415-97-9 320 $aIncludes bibliographical references and index. 327 $aPreface; 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 327 $a7.3 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 327 $aE.5 Paley-Wiener TheoremsBibliography; Index 330 $aA 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 606 $aCalculus 606 $aMathematics 608 $aElectronic books. 615 0$aCalculus. 615 0$aMathematics. 676 $a515 700 $aBosch$b Carlos$0136133 701 $aSwartz$b Charles$054079 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910462800503321 996 $aFunctional calculi$91982126 997 $aUNINA