Spectral Theory on the S-Spectrum for Quaternionic Operators

Description

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. 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