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.

Presents original research previously unpublished Closes a gap in research Develops quaternionic spectral theory

Autorentext

Daniel Alpay, Foster G. and Mary McGaw Professorship in Mathematical Sciences, Chapman University Fabrizio Colombo is professor at the Politecnico di Milano, Italy. Irene Sabadini is professor at the Politecnico di Milano, Italy.

Inhalt
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 H1 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.