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Functional Calculi

Functional Calculi

Hardcover

CalculusGeneral Mathematics

ISBN10: 9814415979
ISBN13: 9789814415972
Publisher: World Scientific Publishing Company
Published: Apr 6 2013
Pages: 228
Weight: 1.20
Height: 0.80 Width: 6.00 Depth: 9.00
Language: English
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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Calculus