The fourfold way in real analysis : an alternative to the metaplectic representation
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The fourfold way in real analysis : an alternative to the metaplectic representation
Resource Information
The work The fourfold way in real analysis : an alternative to the metaplectic representation represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 The fourfold way in real analysis : an alternative to the metaplectic representation
 Title remainder
 an alternative to the metaplectic representation
 Statement of responsibility
 André Unterberger
 Subject

 Analyse harmonique
 Espace des phases (Physique statistique)
 Espaces à produit scalaire
 Fourier Analysis
 Fourier analysis
 Fourier analysis
 Fourier analysis
 Fourier analysis
 Fourier, Analyse de
 Functions of a Complex Variable
 Harmonic analysis
 Harmonic analysis
 Harmonic analysis
 Harmonic analysis
 Inner product spaces
 Inner product spaces
 Inner product spaces
 Inner product spaces
 Lie groups
 Lie groups
 Lie groups
 Lie groups
 Lie, Groupes de
 MATHEMATICS  Infinity
 Mathematical Methods in Physics
 Mathematics
 Phase space (Statistical physics)
 Phase space (Statistical physics)
 Phase space (Statistical physics)
 Phase space (Statistical physics)
 Topological Groups, Lie Groups
 Abstract Harmonic Analysis
 Language
 eng
 Summary
 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 parameterdependent 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 pseudoHilbert space, on which a new translationinvariant integral still exists. All this extends to the ndimensional 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
 Cataloging source
 GW5XE
 Dewey number
 515/.2433
 Index
 index present
 LC call number
 QA403.5
 LC item number
 .U58 2006eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 NLM call number
 Online Book
 Series statement
 Progress in mathematics
 Series volume
 v. 250
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 The fourfold way in real analysis : an alternative to the metaplectic representation, André Unterberger
 The fourfold way in real analysis : an alternative to the metaplectic representation, André Unterberger
 The fourfold way in real analysis : an alternative to the metaplectic representation, André Unterberger
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