Spectral Theory on the S-Spectrum for Quaternionic Operators

• Main Authors: Colombo, Fabrizio (Author, http://id.loc.gov/vocabulary/relators/aut), Gantner, Jonathan (http://id.loc.gov/vocabulary/relators/aut), Kimsey, David P. (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
• Edition: 1st ed. 2018.
• Series: Operator Theory: Advances and Applications, 270
• Subjects: Operator theory.; Dynamics.; Ergodic theory.; Functional analysis.; Operator Theory.; Dynamical Systems and Ergodic Theory.; Functional Analysis.
• Physical Description: IX, 356 p. online resource.
• ISBN: 9783030030742
• ISSN: 0255-0156 ;
• DOI: 10.1007/978-3-030-03074-2

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.