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Mathematics

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B2B & B2C

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.

Functional Calculi

POST SECONDARY FOUR YEAR

COLFR

COLJR

COLSO

COLSR

FUNCTIONAL CALCULI

Duration

Duration Unit Of Measure

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Front Cover.
Half Title Page.
Title Page.
Copyright Page.
Preface.
Contents.
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&#x0027;s Functional Calculus.
The Orlicz&#x2013;Pettis Theorem.
The Spectrum of an Operator.
Self Adjoint, Normal and Unitary Operators.
Sesquilinear Functionals.
Tempered Distributions and the Fourier Transform.
Bibliography.
Index.

Functional Calculi.css-1p8rvzy{position:absolute;padding-left:8px;}

Functional Calculi