# 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 $\ZZ/p\ZZ$.
Document type :
Journal articles

Cited literature [7 references]

https://hal.archives-ouvertes.fr/hal-00466459
Contributor : Aline Bonami <>
Submitted on : Wednesday, October 2, 2013 - 12:32:59 PM
Last modification on : Tuesday, December 8, 2020 - 10:32:11 AM
Long-term archiving on: : Friday, April 7, 2017 - 5:10:31 AM

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### Identifiers

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

### Citation

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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