Item description for The Fourfold Way in Real Analysis: An Alternative to the Metaplectic Representation (Progress in Mathematics) by André Unterberger...
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 numbermodulo 2, the classical case being obtained when itis 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 R2nthat 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 analysisin general,in harmonic analysis,or in mathematical physics.
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Est. Packaging Dimensions: Length: 9.1" Width: 6.2" Height: 0.7" Weight: 0.5 lbs.
Release Date Apr 28, 2006
Publisher Birkhäuser Basel
ISBN 3764375442 ISBN13 9783764375447
Availability 108 units. Availability accurate as of Oct 22, 2016 04:54.
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