Illinois Journal of Mathematics

A weak qualitative uncertainty principle for compact groups

Gitta Kutyniok

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Abstract

For locally compact abelian groups it is known that if the product of the measures of the support of an $L^1$-function $f$ and its Fourier transform is less than $1$, then $f = 0$ almost everywhere. This is a weak version of the classical qualitative uncertainty principle. In this paper we focus on compact groups. We obtain conditions on the structure of a compact group under which there exists a lower bound for all products of the measures of the support of an integrable function and its Fourier transform, and conditions under which this bound equals $1$. For several types of compact groups, we determine the exact set of values which the product can attain.

Article information

Source
Illinois J. Math., Volume 47, Number 3 (2003), 709-724.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138189

Digital Object Identifier
doi:10.1215/ijm/1258138189

Mathematical Reviews number (MathSciNet)
MR2007232

Zentralblatt MATH identifier
1031.43003

Subjects
Primary: 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
Secondary: 43A25: Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups

Citation

Kutyniok, Gitta. A weak qualitative uncertainty principle for compact groups. Illinois J. Math. 47 (2003), no. 3, 709--724. doi:10.1215/ijm/1258138189. https://projecteuclid.org/euclid.ijm/1258138189


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