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Equality cases for the uncertainty principle in finite Abelian groups

Abstract : 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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Submitted on : Wednesday, October 2, 2013 - 12:32:59 PM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Document(s) archivé(s) le : Friday, April 7, 2017 - 5:10:31 AM

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  • HAL Id : hal-00466459, version 2
  • ARXIV : 1003.5060

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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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