Abstract
The first part of this article is an introduction to uncertainty principles in Fourier analysis, while the second summarizes some recent work by the authors and also by Michael Cowling and the authors.
The following (rather vague) principle is well known to every student of classical Fourier analysis: If a function $f$ is 'concentrated' then its Fourier transform $f$ is 'spread out' and vice-versa. After reviewing three precise (and different) formulations of this principle in classical Fourier analysis on $R^n$, we will describe how it extends to LCA groups and certain nonabelian Lie groups - for instance, semisimple Lie groups and Heisenberg groups.
Information
Published: 1 January 1987
First available in Project Euclid: 18 November 2014
zbMATH: 0635.43002
MathSciNet: MR935604
Rights: Copyright © 1987, Centre for Mathematical Analysis, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.
