Spectral Theory on the S-Spectrum for Quaternionic Operators

1. Auflage 2018
ISBN: 978-3-030-03073-5
Verlag: Springer International Publishing

Buch, Englisch, Band 270, 356 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 717 g

Reihe: Operator Theory: Advances and Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Colombo, Fabrizio

Kimsey, David P.

Gantner, Jonathan

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme

Inhaltsverzeichnis

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.