Spectral Properties of Noncommuting Operators

• Main Author: Jefferies, Brian R. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004.
• Edition: 1st ed. 2004.
• Series: Lecture Notes in Mathematics, 1843
• Subjects: Mathematical analysis.; Analysis (Mathematics).; Operator theory.; Functions of complex variables.; Fourier analysis.; Analysis.; Operator Theory.; Functions of a Complex Variable.; Fourier Analysis.
• Physical Description: VII, 184 p. online resource.
• ISBN: 9783540707462
• ISSN: 0075-8434 ;
• DOI: 10.1007/b97327

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.