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À une famille de fonctions positives sur un groupe abélien localement compact, on associe l’ensemble des fonctions qui sont de carré sommable sur par rapport à pour au moins un . Sous certaines conditions simples, portant sur , c’est une algèbre de convolution, contenue dans . On étudie particulièrement le cas droite réelle, ensemble des fonctions paires, sommables, décroissantes sur . Une caractérisation explicite de (ensemble des transformées de Fourier des ) est alors donnée,...
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