Convolution weights on ℓ2-spaces

Autor: Thomas Ransford, Frédéric Morneau-Guérin
Rok vydání: 2020
Předmět:
Zdroj: Journal of Mathematical Analysis and Applications. 492:124396
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2020.124396
Popis: It is known that the weighted L p -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 L p -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.
Databáze: OpenAIRE
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