Functional Calculi, 1st Edition

  • Published By: World Scientific Publishing Company
  • ISBN-10: 9814415987
  • ISBN-13: 9789814415989
  • DDC: 515.7
  • Grade Level Range: College Freshman - College Senior
  • 228 Pages | eBook
  • Original Copyright 2013 | Published/Released January 2015
  • This publication's content originally published in print form: 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.

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
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.
The Orlicz–Pettis Theorem.
The Spectrum of an Operator.
Self Adjoint, Normal and Unitary Operators.
Sesquilinear Functionals.
Tempered Distributions and the Fourier Transform.