We set up a new general coorbit space theory for reproducing representations of a locally compact second countable group G that are not necessarily irreducible nor integrable. Our basic assumption is that the kernel associated with the voice transform belongs to a Fréchet space (Formula presented.) of functions on G, which generalizes the classical choice (Formula presented.). Our basic example is (Formula presented.), or a weighted versions of it. By means of this choice it is possible to treat, for instance, Paley-Wiener spaces and coorbit spaces related to Shannon wavelets and Schrödingerlets.
Coorbit Spaces with Voice in a Fréchet Space
DE MARI CASARETO DAL VERME, FILIPPO;DE VITO, ERNESTO;
2017-01-01
Abstract
We set up a new general coorbit space theory for reproducing representations of a locally compact second countable group G that are not necessarily irreducible nor integrable. Our basic assumption is that the kernel associated with the voice transform belongs to a Fréchet space (Formula presented.) of functions on G, which generalizes the classical choice (Formula presented.). Our basic example is (Formula presented.), or a weighted versions of it. By means of this choice it is possible to treat, for instance, Paley-Wiener spaces and coorbit spaces related to Shannon wavelets and Schrödingerlets.
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