An introduction to the uncertainty principle : Hardy's theorem on Lie groups /
However, this text goes well beyond Hardy-type theorems to develop deeper connections among the fields of abstract harmonic analysis, concrete hard analysis, Lie theory, and special functions, and to study the fascinating interplay between the noncompact groups that underlie the geometric objects in...
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| Format: | eBook |
| Language: | English |
| Published: |
Boston :
Birkhäuser,
[2004]
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| Series: | Progress in mathematics (Boston, Mass.) ;
v. 217. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | However, this text goes well beyond Hardy-type theorems to develop deeper connections among the fields of abstract harmonic analysis, concrete hard analysis, Lie theory, and special functions, and to study the fascinating interplay between the noncompact groups that underlie the geometric objects in question and the compact rotation groups that act as symmetries of these objects." "A tutorial introduction is given to the necessary background material. The first chapter deals with theorems of Hardy and Beurling for the Euclidean Fourier transform; the second chapter establishes several versions of Hardy's Theorem for the Fourier transform on the Heisenberg group and characterizes the heat kernal for the sublaplacian. In Chapter three, the Helgason Fourier transform on rank one symmetric spaces is treated. Most of the results presented here are valid in the general context of solvable extensions of H-type groups." "The techniques used to prove the main results run the gamut of modern harmonic analysis: they include representation theory, spherical functions, Hecke-Bochner formulas and special functions. Graduate students and researchers in harmonic analysis will benefit from this unique work."--Jacket. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xii, 174 pages) |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliography: | Includes bibliographical references (pages 169-172) and index. |
| ISBN: | 9780817681647 (electronic bk.) 0817681647 (electronic bk.) |