A weak qualitative uncertainty principle for compact groups

Kutyniok, Gitta (2003): A weak qualitative uncertainty principle for compact groups. In: Illinois Journal of Mathematics, Vol. 47, No. 3: pp. 709-724

Abstract

For locally compact abelian groups it is known that if the product of the measures of the support of an L1-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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0019-2082
• Language: English