Functional calculi

Carlos Bosch, Charles Swartz

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.

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  • Vector and Operator Valued Measures
  • Functions of a Self Adjoint Operator
  • Functions of Several Commuting Self Adjoint Operators
  • The Spectral Theorem for Normal Operators
  • Integrating Vector Valued Functions
  • An Abstract Functional Calculus
  • The Riesz Operational Calculus
  • Weyl's Functional Calculus
  • Appendices: The Orlicz - Pettis Theorem
  • The Spectrum of an Operator
  • Self Adjoint, Normal and Unitary Operators
  • Sesquilinear Functionals
  • Tempered Distributions and the Fourier Transform.

「Nielsen BookData」より


書名 Functional calculi
著作者等 Bosch Giral, Carlos
Swartz, Charles
Bosch Carlos
出版元 World Scientific
刊行年月 c2013
ページ数 x, 215 p.
大きさ 24 cm
ISBN 9789814415972
NCID BB12890008
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言語 英語
出版国 シンガポール