Functional Calculi by Carlos Bosch

Functional Calculi

byCarlos Bosch, Charles Swartz

Kobo ebook | March 26, 2013

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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.

Contents:

  • 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

Readership: Graduate students, mathematicians, physicists or engineers interested in functions of operators.

Title:Functional CalculiFormat:Kobo ebookPublished:March 26, 2013Publisher:World Scientific Publishing CompanyLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9814415995

ISBN - 13:9789814415996

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