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

Morneau-Guérin, Frédéric, & 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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Item Type: Journal Articles
Refereed: Yes
Status: Published
Abstract: 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.
Depositor: Morneau-Guérin, Frédéric
Owner / Manager: Frédéric Morneau-Guérin
Deposited: 03 Apr 2020 17:12
Last Modified: 24 Jul 2020 10:56

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