no. 4
The norm of the Fourier transform on finite abelian groups
[La norme de la transformée de Fourier sur les groupes abéliens finis]
Gilbert, John1 ; Rzeszotnik, Ziemowit2
1 University of Texas Department of Mathematics Austin, TX 78712–1082 (USA)
2 Wrocław University Mathematical Institute Pl. Grunwaldzki 2/4 50-384 Wrocław (Poland)
Annales de l'Institut Fourier, Tome 60 (2010) no. 4, pp. 1317-1346.

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.

For 1≤p,q≤∞ 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.

DOI : 10.5802/aif.2556
Classification : 42C40, 43A15, 43A25
Keywords: Fourier transform, finite abelian groups, wave packets, biunimodular functions
Mot clés : transformée de Fourier, groupes abéliens finis, paquets d’ondes, fonctions bi-unimodulaires
Gilbert, John 1 ; Rzeszotnik, Ziemowit 2

1 University of Texas Department of Mathematics Austin, TX 78712–1082 (USA)
2 Wrocław University Mathematical Institute Pl. Grunwaldzki 2/4 50-384 Wrocław (Poland) 
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Gilbert, John; Rzeszotnik, Ziemowit. The norm of the Fourier transform on finite abelian groups. Annales de l'Institut Fourier, Tome 60 (2010) no. 4, pp. 1317-1346. doi : 10.5802/aif.2556. https://aif.centre-mersenne.org/articles/10.5802/aif.2556/

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