Progress in Mathematics
cover

The Fourfold Way in Real Analysis

An Alternative to the Metaplectic Representation

Authors: Unterberger, André

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About this book

The fourfold way starts with the consideration of entire functions of one variable satisfying specific estimates at infinity, both on the real line and the pure imaginary line. A major part of classical analysis, mainly that which deals with Fourier analysis and related concepts, can then be given a parameter-dependent analogue. The parameter is some real number modulo 2, the classical case being obtained when it is an integer. The space L2(R) has to give way to a pseudo-Hilbert space, on which a new translation-invariant integral still exists. All this extends to the n-dimensional case, and in the alternative to the metaplectic representation so obtained, it is the space of Lagrangian subspaces of R2n that plays the usual role of the complex Siegel domain. In fourfold analysis, the spectrum of the harmonic oscillator can be an arbitrary class modulo the integers.

Even though the whole development touches upon notions of representation theory, pseudodifferential operator theory, and algebraic geometry, it remains completely elementary in all these aspects. The book should be of interest to researchers working in analysis in general, in harmonic analysis, or in mathematical physics.

Table of contents (4 chapters)

Table of contents (4 chapters)
  • The One-dimensional Anaplectic Representation

    Pages 1-44

  • The n-dimensional Anaplectic Analysis

    Pages 45-146

  • Towards the Anaplectic Symbolic Calculi

    Pages 147-184

  • The One-dimensional Case Revisited

    Pages 185-215

Buy this book

eBook $89.00
price for USA in USD (gross)
  • ISBN 978-3-7643-7545-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-3-7643-7544-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Fourfold Way in Real Analysis
Book Subtitle
An Alternative to the Metaplectic Representation
Authors
Series Title
Progress in Mathematics
Series Volume
250
Copyright
2006
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-7545-4
DOI
10.1007/3-7643-7545-0
Hardcover ISBN
978-3-7643-7544-7
Series ISSN
0743-1643
Edition Number
1
Number of Pages
X, 222
Topics