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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[目次]

  • 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.

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この本の情報

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
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