Functional Calculi

By Charles Swartz and CHARLES W 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.

• Format: Hardcover
• Language: English
• ISBN: 9814415979
• ISBN13: 9789814415972
• Release Date: May 2013
• Publisher: World Scientific Publishing Company
• Length: 228 Pages
• Weight: 1.20 lbs.
• Dimensions: 0.8" x 6.0" x 9.0"