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hal-00466459, version 1

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

Aline Bonami () 1, Saifallah Ghobber () 12

(2010-03-23)

Abstract: 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 $\ZZ/p\ZZ$.

• 1:  Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO)
• Université d'Orléans – CNRS : UMR7349
• 2:  Analyse harmonique et fonctions spéciales
• Faculté des Sciences de Tunis
• Domain : Mathematics/Classical Analysis and ODEs

• hal-00466459, version 1
• oai:hal.archives-ouvertes.fr:hal-00466459
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• Submitted on: Tuesday, 23 March 2010 21:21:26
• Updated on: Friday, 26 March 2010 08:56:25