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Jean-Pierre Gazeau; Jean-Louis Verger-Gaugry
Diffraction spectra of weighted Delone sets on beta-lattices with beta a quadratic unitary Pisot number
(Spectre de diffraction d’ensembles de Delaunay avec poids supportés par des beta-réseaux où beta est un nombre de Pisot unitaire)
Annales de l'institut Fourier, 56 no. 7 (2006), p. 2437-2461, doi: 10.5802/aif.2245
Article PDF | Analyses MR 2290786 | Zbl 1119.52015 | 3 citations dans Cedram
Class. Math.: 52C23, 78A45, 42A99
Mots clés: Ensembles de Delaunay, ensembles de Meyer, beta-entiers, beta-réseaux, nombres de Pisot-Vijayaraghavan, diffraction mathématique

Résumé - Abstract

On caractérise au moyen de la théorie des distributions la transformée de Fourier d’un peigne de Dirac avec poids, plus particulièrement la partie purement ponctuelle qui correspond aux pics de Bragg dans le spectre de diffraction. La fonction intensité de ces derniers est donnée d’une manière explicite. On en déduit le spectre de diffraction d’ensembles de Delaunay avec poids supportés par les beta-réseaux dans le cas où le poids est factorisable et où beta est le nombre d’or.

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