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Spectral Properties of Noncommuting Operators

  • Authors
  • Brian Jefferies

Part of the Lecture Notes in Mathematics book series (LNM, volume 1843)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Brian Jefferies
    Pages 1-11
  3. Brian Jefferies
    Pages 13-25
  4. Brian Jefferies
    Pages 27-38
  5. Brian Jefferies
    Pages 67-121
  6. Brian Jefferies
    Pages 157-171
  7. Brian Jefferies
    Pages 173-179
  8. Back Matter
    Pages 181-184

About this book

Introduction

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.

Keywords

Feynman's operational calculus Weyl calculus calculus differential equation functional calculus joint spectrum monogenic function

Bibliographic information

  • DOI https://doi.org/10.1007/b97327
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-21923-1
  • Online ISBN 978-3-540-70746-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site