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Colombo F., Gantner J., Kimsey D.P. Spectral Theory on the S-Spectrum for Quaternionic Operators

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Colombo F., Gantner J., Kimsey D.P. Spectral Theory on the S-Spectrum for Quaternionic Operators
Springer, 2019. — 357 p. — (Operator Theory: Advances and Applications 270). —ISBN 3030030733.
The subject of this monograph is the quaternionic spectral theory based on the notion of S-spectrum. With the purpose of giving a systematic and self-contained treatment of this theory that has been developed in the last decade, the book features topics like the S-functional calculus, the F-functional calculus, the quaternionic spectral theorem, spectral integration and spectral operators in the quaternionic setting. These topics are based on the notion of S-spectrum of a quaternionic linear operator. Further developments of this theory lead to applications in fractional diffusion and evolution problems that will be covered in a separate monograph.
Table of contents
Introduction
Slice Hyperholomorphic Functions
The S-Spectrum and the S-Functional Calculus
Properties of the S-Functional Calculus for Bounded Operators
The S-Functional Calculus for Unbounded Operators
The H∞-Functional Calculus
The F-Functional Calculus for Bounded Operators
The F-Functional Calculus for Unbounded Operators
Quaternionic Operators on a Hilbert Space
Spectral Integrals
The Spectral Theorem for Bounded Normal Operators
The Spectral Theorem for Unbounded Normal Operators
Spectral Theorem for Unitary Operators
Spectral Integration in the Quaternionic Setting
Bounded Quaternionic Spectral Operators
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