The norm of the Fourier transform on finite abelian groups

[La norme de la transformée de Fourier sur les groupes abéliens finis]

Gilbert, John ; Rzeszotnik, Ziemowit

Annales de l'Institut Fourier, Tome 60 (2010), p. 1317-1346 / Harvested from Numdam

Résumé

Pour les valeurs de $p$ et $q$ comprises entre $1$ et l’infini, nous déterminons la norme de la transformée de Fourier de l’espace $L^p$ d’un groupe abélien fini vers l’espace $L^q$ du groupe dual.

Abstract

For $1\le p,q\le \infty $ we calculate the norm of the Fourier transform from the $L^p$ space on a finite abelian group to the $L^q$ space on the dual group.

Détail

Publié le : 2010-01-01

MR 2722243 | Zbl 1202.42065 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/aif.2556
Classification:  42C40,  43A15,  43A25
Mots clés: transformée de Fourier, groupes abéliens finis, paquets d’ondes, fonctions bi-unimodulaires

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