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The Donoho-Stark uncertainty principle for a finite abelian group. (English) Zbl 1100.43003
Summary: Let $A$ be a finite cyclic group and let $f$ be a non-zero complex valued function defined on $A$. Donoho and Stark have an elementary proof that the product of the cardinality of the support of $f$ and the cardinality of the support of the Fourier transform of $f$ is greater than or equal to the order of $A$. They also describe the set of functions for which equality holds. We provide an elementary proof of a generalization of these results to the case when $A$ is an arbitrary finite abelian group.

MSC:
43A70Analysis on specific locally compact and other abelian groups
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