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  • Book
  • © 2004

Spectral Properties of Noncommuting Operators

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

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-VIII
  2. 1. Introduction

    • Brian Jefferies
    Pages 1-11
  3. 2. Weyl Calculus

    • Brian Jefferies
    Pages 13-25
  4. 3. Clifford Analysis

    • Brian Jefferies
    Pages 27-38
  5. 5. The Joint Spectrum of Matrices

    • Brian Jefferies
    Pages 67-121
  6. 7. Feynman’s Operational Calculus

    • Brian Jefferies
    Pages 157-171
  7. References

    • Brian Jefferies
    Pages 173-179
  8. Back Matter

    Pages 181-184

About this book

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

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions