**
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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