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hal-00466459, version 1

Equality cases for the uncertainty principle in finite Abelian groups

Aline Bonami () 1, Saifallah Ghobber () 1, 2

(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
  • http://hal.archives-ouvertes.fr/hal-00466459
  • oai:hal.archives-ouvertes.fr:hal-00466459
  • From: Bonami Aline <>
  • Submitted on: Tuesday, 23 March 2010 21:21:26
  • Updated on: Friday, 26 March 2010 08:56:25