Spectral Theory on the S-Spectrum for Quaternionic Operators

✍ Scribed by Fabrizio Colombo, Jonathan Gantner, David P. Kimsey

• Publisher: Springer International Publishing;Birkhäuser
• Year: 2018
• Tongue: English
• Leaves: 357
• Series: Operator Theory: Advances and Applications 270
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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

Front Matter ....Pages i-ix
Introduction (Fabrizio Colombo, Jonathan Gantner, David P. Kimsey)....Pages 1-10
Slice Hyperholomorphic Functions (Fabrizio Colombo, Jonathan Gantner, David P. Kimsey)....Pages 11-51
The S-Spectrum and the S-Functional Calculus (Fabrizio Colombo, Jonathan Gantner, David P. Kimsey)....Pages 53-74
Properties of the S-Functional Calculus for Bounded Operators (Fabrizio Colombo, Jonathan Gantner, David P. Kimsey)....Pages 75-124
The S-Functional Calculus for Unbounded Operators (Fabrizio Colombo, Jonathan Gantner, David P. Kimsey)....Pages 125-136
The H∞-Functional Calculus (Fabrizio Colombo, Jonathan Gantner, David P. Kimsey)....Pages 137-149
The F-Functional Calculus for Bounded Operators (Fabrizio Colombo, Jonathan Gantner, David P. Kimsey)....Pages 151-176
The F-Functional Calculus for Unbounded Operators (Fabrizio Colombo, Jonathan Gantner, David P. Kimsey)....Pages 177-185
Quaternionic Operators on a Hilbert Space (Fabrizio Colombo, Jonathan Gantner, David P. Kimsey)....Pages 187-217
Spectral Integrals (Fabrizio Colombo, Jonathan Gantner, David P. Kimsey)....Pages 219-231
The Spectral Theorem for Bounded Normal Operators (Fabrizio Colombo, Jonathan Gantner, David P. Kimsey)....Pages 233-243
The Spectral Theorem for Unbounded Normal Operators (Fabrizio Colombo, Jonathan Gantner, David P. Kimsey)....Pages 245-254
Spectral Theorem for Unitary Operators (Fabrizio Colombo, Jonathan Gantner, David P. Kimsey)....Pages 255-271
Spectral Integration in the Quaternionic Setting (Fabrizio Colombo, Jonathan Gantner, David P. Kimsey)....Pages 273-302
Bounded Quaternionic Spectral Operators (Fabrizio Colombo, Jonathan Gantner, David P. Kimsey)....Pages 303-335
Back Matter ....Pages 337-356

✦ Subjects

Mathematics; Operator Theory; Dynamical Systems and Ergodic Theory; Functional Analysis