ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXIII, 2 (2004)
p. 155 – 160
The Donoho – Stark Uncertainty Principle for a Finite Abelian Group
E. Matusiak, M. Ozaydin and T. Przebinda
Abstract.
Let $A$ be a finite cyclic group and let $f$ be a non-zero
complex valued function defined on $A$.
Donoho and Stark gave 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 described the set of functions for which the equality holds.
We provide an elementary proof of a~generalization these results to the
case when $A$ is an arbitrary finite abelian group.
AMS Subject classification: 43A70; Secondary: 11T99, 22B99, 42C99.
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