An Introduction to the Uncertainty Principle

Hardy’s Theorem on Lie Groups

  • Sundaram Thangavelu

Part of the Progress in Mathematics book series (PM, volume 217)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Sundaram Thangavelu
    Pages 1-43
  3. Sundaram Thangavelu
    Pages 45-104
  4. Sundaram Thangavelu
    Pages 105-168
  5. Back Matter
    Pages 169-177

About this book

Introduction

Motivating this interesting monograph is the development of a number of analogs of Hardy's theorem in settings arising from noncommutative harmonic analysis. This is the central theme of this work.
Specifically, it is devoted to connections among various theories arising from abstract harmonic analysis, concrete hard analysis, Lie theory, special functions, and the very interesting 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 second chapter establishes several versions of Hardy's theorem for the Fourier transform on the Heisenberg group and characterizes the heat kernel 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 such as representation theory, spherical functions, Hecke-Bochner formulas and special functions.
Graduate students and researchers in harmonic analysis will greatly benefit from this book.

Keywords

Fourier transfoms Fourier transform abstract harmonic analysis harmonic analysis several complex variables

Authors and affiliations

  • Sundaram Thangavelu
    • 1
  1. 1.Statistics and Mathematics DivisionIndian Statistical InstituteBangaloreIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8164-7
  • Copyright Information Birkhäser Boston 2004
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6468-2
  • Online ISBN 978-0-8176-8164-7
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • About this book