Spectral Properties of Noncommuting Operators

2004
ISBN: 978-3-540-21923-1
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1843, 184 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 306 g

Reihe: Lecture Notes in Mathematics

Forming functions of operators is a basic task of many areas of linear analysis and quantum physics. Weyl’s functional calculus, initially applied to the position and momentum operators of quantum mechanics, also makes sense for finite systems of selfadjoint operators. By using the Cauchy integral formula available from Clifford analysis, the book examines how functions of a finite collection of operators can be formed when the Weyl calculus is not defined. The technique is applied to the determination of the support of the fundamental solution of a symmetric hyperbolic system of partial differential equations and to proving the boundedness of the Cauchy integral operator on a Lipschitz surface.

Zielgruppe

Research

Autoren/Hrsg.

Jefferies, Brian R.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

Introduction.- Weyl Calculus.- Clifford Analysis.- Functional Calculus for Noncommuting Operators.- The Joint Spectrum of Matrices.- The Monogenic Calculus for Sectorial Operators.- Feynman's Operational Calculus.- References.- Index.