Convolution weights on l^2-spaces [r-libre/1941]

Morneau-Guérin, Frédéric et Ransford, Thomas (2020). Convolution weights on l^2-spaces. The Journal of Mathematical Analysis and Applications, 492 (1). https://doi.org/10.1016/j.jmaa.2020.124396

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Catégorie de document :	Articles de revues
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Étape de publication :	Publié
Résumé :	It is known that the weighted Lp-space on a locally compact group is stable with respect to convolution if the weight function satisfies a certain type of convolution inequality. There are several counterexamples showing that this sufficient condition is not necessary. However, for one class of groups, namely discrete abelian groups, no such counterexample is known. Thus there remains the possibility that the convolution inequality truly characterizes stability of convolution for weighted Lp-spaces on these groups. In this paper, we investigate this inequality and, in the case p=2, reinterpret it in the light of operator theory and in the context of the theory of reproducing kernel Hilbert spaces.
Adresse de la version officielle :	https://www.sciencedirect.com/science/article/abs/...
Déposant:	Morneau-Guérin, Frédéric
Responsable :	Frédéric Morneau-Guérin
Dépôt :	03 avr. 2020 17:12
Dernière modification :	18 déc. 2020 14:43

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