• Uncertainty principles on certain Lie groups

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/105/02/0135-0151

• # Keywords

Fourier transform; Heisenberg group; motion group; uncertainty principle

• # Abstract

There are several ways of formulating the uncertainty principle for the Fourier transform on ℝn. Roughly speaking, the uncertainty principle says that if a functionf is ‘concentrated’ then its Fourier transform$$\tilde f$$ cannot be ‘concentrated’ unlessf is identically zero. Of course, in the above, we should be precise about what we mean by ‘concentration’. There are several ways of measuring ‘concentration’ and depending on the definition we get a host of uncertainty principles. As several authors have shown, some of these uncertainty principles seem to be a general feature of harmonic analysis on connected locally compact groups. In this paper, we show how various uncertainty principles take form in the case of some locally compact groups including ℝn, the Heisenberg group, the reduced Heisenberg groups and the Euclidean motion group of the plane.

• # Author Affiliations

1. Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile, Mysore Road, Bangalore - 560 059, India

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019