Functional calculi

Functional calculi / Carlos Bosch, Charles 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 s...

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Bibliographic Details
Main Author: Bosch, Carlos
Other Authors: Swartz, Charles
Format: eBook
Language:English
Published: Singapore : World Scientific, ©2013.
Subjects:
Functional analysis.
Calculus.
Mathematics.
calculus.
mathematics.
applied mathematics.
MATHEMATICS > Calculus.
MATHEMATICS > Mathematical Analysis.
Functional analysis
Online Access:Click for online access
Table of Contents:
  • 1. Vector and operator valued measures. 1.1. Vector measures. 1.2. Operator valued measures. 1.3. Extensions of measures. 1.4. Regularity and countable additivity. 1.5. Countable additivity on products
  • 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. 5.1. Vector valued measurable functions. 5.2. Integrating vector valued functions
  • 6. An abstract functional calculus
  • 7. The Riesz operational calculus. 7.1. Power series. 7.2. Laurent series. 7.3. Runge's theorem. 7.4. Several complex variables. 7.5. Riesz operational calculus. 7.6. Abstract functional calculus. 7.7. Spectral sets. 7.8. Isolated points. 7.9. Wiener's theorem
  • 8. Weyl's functional calculus.

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