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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