## Proceedings of the Centre for Mathematics and its Applications

### Some uncertainty principles in abstract harmonic analysis

#### 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.

#### Article information

Dates
First available in Project Euclid: 18 November 2014