Proceedings of the Centre for Mathematics and its Applications

Some uncertainty principles in abstract harmonic analysis

John F. Price and Alladi Sitaram

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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.

Article information

Miniconference on Harmonic Analysis. M Cowling, C Meaney, and W Moran, eds. Proceedings of the Centre for Mathematical Analysis, v. 15. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1987), 208-213

First available in Project Euclid: 18 November 2014

Permanent link to this document euclid.pcma/1416336469

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Price, John F.; Sitaram, Alladi. Some uncertainty principles in abstract harmonic analysis. Miniconference on Harmonic Analysis, 208--213, Centre for Mathematical Analysis, The Australian National University, Canberra AUS, 1987.

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