Fabrizio Colombo, Jonathan Gantner, David P. Kimsey

Spectral Theory on the S-Spectrum for Quaternionic Operators (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer International Publishing
• Seitenzahl: 356
• Erscheinungstermin: 4. Januar 2019
• Englisch
• ISBN-13: 9783030030742
• Artikelnr.: 54880259

Inhaltsangabe

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.