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Article Dans Une Revue Acta Scientiarum Mathematicarum Année : 2013

Equality cases for the uncertainty principle in finite Abelian groups

Résumé

We consider the families of finite Abelian groups $\ZZ/p\ZZ\times \ZZ/p\ZZ$, $\ZZ/p^2\ZZ$ and $\ZZ/p\ZZ\times \ZZ/q\ZZ$ for $p,q$ two distinct prime numbers. For the two first families we give a simple characterization of all functions whose support has cardinality $k$ while the size of the spectrum satisfies a minimality condition. We do it for a large number of values of $k$ in the third case. Such equality cases were previously known when $k$ divides the cardinality of the group, or for groups $\ZZ/p\ZZ$.
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Dates et versions

hal-00466459 , version 1 (23-03-2010)
hal-00466459 , version 2 (02-10-2013)

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Citer

Aline Bonami, Saifallah Ghobber. Equality cases for the uncertainty principle in finite Abelian groups. Acta Scientiarum Mathematicarum, 2013, 79 (3), pp.507-528. ⟨hal-00466459v2⟩
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