反馈文件质量
lgli/D:\!genesis\library.nu\f1\_284598.f17a83bc5aff8a3af4f049047f4a5b55.pdf
The fourfold way in real analysis an alternative to the metaplectic representation The fourfold way in real analysis : an alternative to the metaplectic representation 🔍
André Unterberger (auth.) Birkhäuser-Verlag, Progress in Mathematics, Progress in Mathematics 250, 1, 2006
英语 [en] · PDF · 2.3MB · 2006 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/scihub/zlib · Save
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 itis 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 mathematical physics.
备用文件名
lgrsnf/D:\!genesis\library.nu\f1\_284598.f17a83bc5aff8a3af4f049047f4a5b55.pdf
备用文件名
nexusstc/The Fourfold Way In Real Analysis/f17a83bc5aff8a3af4f049047f4a5b55.pdf
备用文件名
scihub/10.1007/3-7643-7545-0.pdf
备用文件名
zlib/Mathematics/André Unterberger (auth.)/The Fourfold Way In Real Analysis: An Alternative to the Metaplectic Representation_876525.pdf
备选标题
The Fourfold Way in Real Analysis: An Alternative to the Metaplectic Representation (Progress in Mathematics, 250)
备选作者
Unterberger, André
备选作者
Andre Unterberger
备用出版商
Birkhäuser Verlag, Birkh�auser Verlag
备用出版商
Birkh�auser Verlag Birkhäuser Verlag
备用出版商
Birkhäuser GmbH
备用出版商
Springer Basel
备用版本
Progress in mathematics (Boston, Mass.), v. 250, Basel ; Boston Basel ; Boston, ©2006
备用版本
1 edition, April 2006
备用版本
Germany, Germany
备用版本
2006, US, 2006
元数据中的注释
до 2011-01
元数据中的注释
lg451708
元数据中的注释
{"container_title":"Progress in Mathematics","edition":"1","isbns":["3764375442","9783764375447"],"last_page":222,"publisher":"Birkhäuser-Verlag","series":"Progress in Mathematics 250"}
元数据中的注释
类型: 图书
元数据中的注释
出版日期: 2006
元数据中的注释
出版社: Birkha?user Verlag
元数据中的注释
出版日期: 2006.04
元数据中的注释
出版社: Birkh?user
元数据中的注释
页码: 222
备用描述
The n-dimensionalmetaplectic groupSp(n, R) is the twofoldcoverof the sympl- n n tic group Sp(n, R), which is the group of linear transformations ofX = R R that preserve the bilinear (alternate) form x y [( ), ( )] =? x, ? + y, ? . (0. 1) ? ? 2 n There is a unitary representation of Sp(n, R)intheHilbertspace L (R ), called the metaplectic representation, the image of which is the groupof transformations generated by the following the linear changes of variables, the operators of multiplication by exponentials with pure imaginary quadratic forms in the ex- nent, and the Fourier transformation; some normalization factor enters the de?- tion of the operators of the ?rst and third species. The metaplectic representation was introduced in a great generality in [28] - special cases had been considered before, mostly in papers of mathematical physics - and it is of such fundamental importancethat the two concepts (the groupand the representation)havebecome virtually indistinguishable. This is not going to be our point of indeed, the main point of this work is to show that a certain ?nite covering of the symplectic group (generally of degree n) has another interesting representation, which enjoys analogues of most of the nicer properties of the metaplectic representation. We shall call it the anaplectic representation - other coinages that may come to your mind sound too medical - and shall consider ?rst the one-dimensional case, the main features of which can be described in quite elementary terms.
备用描述
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 mathematical physics.
备用描述
The One-dimensional Anaplectic Representation....Pages 1-44
The n -dimensional Anaplectic Analysis....Pages 45-146
Towards the Anaplectic Symbolic Calculi....Pages 147-184
The One-dimensional Case Revisited....Pages 185-215
备用描述
Progress in Mathematics
Erscheinungsdatum: 17.03.2006
开源日期
2011-06-04
更多信息……

🚀 快速下载

成为会员以支持书籍、论文等的长期保存。为了感谢您对我们的支持，您将获得高速下载权益。❤️

🐢 低速下载

由可信的合作方提供。 更多信息请参见常见问题解答。 （可能需要验证浏览器——无限次下载！）

所有选项下载的文件都相同，应该可以安全使用。即使这样，从互联网下载文件时始终要小心。例如，确保您的设备更新及时。
显示外部下载
  • 对于大文件，我们建议使用下载管理器以防止中断。
    推荐的下载管理器：Motrix
  • 您将需要一个电子书或 PDF 阅读器来打开文件，具体取决于文件格式。
    推荐的电子书阅读器：Anna的档案在线查看器、ReadEra和Calibre
  • 使用在线工具进行格式转换。
    推荐的转换工具：CloudConvert和PrintFriendly
  • 您可以将 PDF 和 EPUB 文件发送到您的 Kindle 或 Kobo 电子阅读器。
    推荐的工具：亚马逊的“发送到 Kindle”和djazz 的“发送到 Kobo/Kindle”
  • 支持作者和图书馆
    ✍️ 如果您喜欢这个并且能够负担得起，请考虑购买原版，或直接支持作者。
    📚 如果您当地的图书馆有这本书，请考虑在那里免费借阅。