Equality cases for the uncertainty principle in finite Abelian groups

Details Equality cases for the uncertainty principle in finite Abelian groups Equality cases for the uncertainty principle in finite Abelian groups

2010-03-26

arxiv.org/abs/1003.5060v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We consider the families of finite Abelian groups $\ZZ/p\ZZ\times \ZZ/q\ZZ$ and $\ZZ/p^2\ZZ$, for $p,q$ prime numbers. We give a simple characterization of all functions $f$ for which the size of the support is at most $k$ and the size of the spectrum is minimal among such functions. Such equality cases were previously known when $k$ divides the cardinal of the group, or for groups $\ZZ/p\ZZ$.

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