The Fourfold Way In Real Analysis : An Alternative to the Metaplectic Representation / by André Unterberger
(Progress in Mathematics ; 250)
| データ種別 | 電子ブック |
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| 出版情報 | Basel : Birkhäuser Basel , 2006 |
| 本文言語 | 英語 |
| 大きさ | X, 222 p : online resource |
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| 内容注記 | The One-dimensional Anaplectic Representation The n-dimensional Anaplectic Analysis Towards the Anaplectic Symbolic Calculi The One-dimensional Case Revisited |
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| 一般注記 | 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 |
| 著者標目 | *Unterberger, André author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Topological groups LCSH:Lie groups LCSH:Harmonic analysis LCSH:Functional analysis LCSH:Functions of complex variables LCSH:Physics FREE:Mathematics FREE:Functional Analysis FREE:Topological Groups, Lie Groups FREE:Mathematical Methods in Physics FREE:Functions of a Complex Variable FREE:Abstract Harmonic Analysis |
| 分 類 | DC23:515.7 |
| 巻冊次 | ISBN:9783764375454 
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| ISBN | 9783764375454 |
| URL | http://dx.doi.org/10.1007/3-7643-7545-0 |
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