An Introduction to the Uncertainty Principle
Hardy's Theorem on Lie Groups (Progress in Mathematics)
1 edition
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Word Count
46,500 words, Guess
Page Count
186 pages
Physical Format
Hardcover
Identifiers
- Open LibraryOL8074811M
- ISBN-139780817643300
- ISBN-100817643303
- OCLC Control Number52232224
- OCLC Control Number52086297
and 2 more
- Library of Congress Control Number2003050228
- Goodreads1943604
Classifications
- LCCQA403 .T52 2004
Description
"The central theme and motivation of this monograph is the development of analogs of Hardy's Theorem in settings that arise from noncommutative harmonic analysis. Specifically, the book is devoted in part to variations of the mathematical Uncertainty Principle - Hardy's Theorem is one interpretation - which states that a function and its Fourier transform cannot simultaneously be very small. 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.
First Sentence
The aim of this chapter is to prove Hardy's theorem for the Euclidean Fourier transform.
Excerpt
The aim of this chapter is to prove Hardy's theorem for the Euclidean Fourier transform.
Subjects
Other Editions
- An Introduction to the Uncertainty Principle: Hardy's Theorem on Lie Groups (Progress in Mathematics)
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