| 书目名称 | The Fourfold Way in Real Analysis | | 副标题 | An Alternative to th | | 编辑 | André Unterberger | | 视频video | | | 概述 | Examines the different, but fully coherent, analysis one could get when trading the usual L2 scalar product for an indefinite one.The new analysis developed here is examined in connection with classic | | 丛书名称 | Progress in Mathematics | | 图书封面 |  | | 描述 | .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 .L.2.(.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 .R.2n. .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 math | | 出版日期 | Book 2006 | | 关键词 | Analysis; Anaplectic representation; Harmonic oscillator; Hilbert space; Metaplectic representation; Oper | | 版次 | 1 | | doi | https://doi.org/10.1007/3-7643-7545-0 | | isbn_ebook | 978-3-7643-7545-4Series ISSN 0743-1643 Series E-ISSN 2296-505X | | issn_series | 0743-1643 | | copyright | Birkhäuser Basel 2006 |
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发表于 2025-3-21 18:34:09
