TY  - BOOK
AU  - Bosch,Carlos
AU  - Swartz,Charles
TI  - Functional calculi
SN  - 9789814415972
U1  - 515.7 23
PY  - 2013///
CY  - Singapore
PB  - World Scientific
KW  - Functional analysis
N1  - 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
N2  - 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 --
ER  -