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.
Citation
Gitta Kutyniok. "A weak qualitative uncertainty principle for compact groups." Illinois J. Math. 47 (3) 709 - 724, Fall 2003. https://doi.org/10.1215/ijm/1258138189
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