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The Resource The Fourfold Way In Real Analysis : An Alternative to the Metaplectic Representation, by André Unterberger, (electronic resource)

The Fourfold Way In Real Analysis : An Alternative to the Metaplectic Representation, by André Unterberger, (electronic resource)

Creator
Contributor
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 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
Language
eng
Work
Publication
Extent
1 online resource (X, 220 p.)
Contents
  • Introduction
  • The One-dimensional Anaplectic Representation
  • The n-dimensional Anaplectic Analysis
  • Towards the Anaplectic Symbolic Calculi
  • The Fourfold Way
  • Bibliography
  • Index.
Isbn
9783764375454
Instance
Label
The Fourfold Way In Real Analysis : An Alternative to the Metaplectic Representation
Title
The Fourfold Way In Real Analysis
Title remainder
An Alternative to the Metaplectic Representation
Statement of responsibility
by André Unterberger
Creator
Contributor
Subject
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 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
Member of
Is part of
http://library.link/vocab/creatorName
Unterberger, André
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink (Online service)
Series statement
Progress in Mathematics
Series volume
250
http://library.link/vocab/subjectName
  • Mathematics
  • Topological Groups
  • Harmonic analysis
  • Functions of complex variables
  • Mathematical physics
Label
The Fourfold Way In Real Analysis : An Alternative to the Metaplectic Representation, by André Unterberger, (electronic resource)
Instantiates
Publication
Contents
Introduction -- The One-dimensional Anaplectic Representation -- The n-dimensional Anaplectic Analysis -- Towards the Anaplectic Symbolic Calculi -- The Fourfold Way -- Bibliography -- Index.
Control code
ssj0000157669
Dimensions
unknown
Extent
1 online resource (X, 220 p.)
Form of item
online
Governing access note
Access restricted to subscribing institutions
Isbn
9783764375454
Other control number
10.1007/3-7643-7545-0
Other physical details
online resource
Specific material designation
remote
System control number
(WaSeSS)ssj0000157669
Label
The Fourfold Way In Real Analysis : An Alternative to the Metaplectic Representation, by André Unterberger, (electronic resource)
Publication
Contents
Introduction -- The One-dimensional Anaplectic Representation -- The n-dimensional Anaplectic Analysis -- Towards the Anaplectic Symbolic Calculi -- The Fourfold Way -- Bibliography -- Index.
Control code
ssj0000157669
Dimensions
unknown
Extent
1 online resource (X, 220 p.)
Form of item
online
Governing access note
Access restricted to subscribing institutions
Isbn
9783764375454
Other control number
10.1007/3-7643-7545-0
Other physical details
online resource
Specific material designation
remote
System control number
(WaSeSS)ssj0000157669

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