Functional calculi / Carlos Bosch, Charles Swartz.

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.

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.

Includes bibliographical references and index.

English.

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