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arXiv · 1402.3917

Coorbit spaces with voice in a Fréchet space

Stephan Dahlke·Filippo De Mari·Ernesto De Vito·Demetrio Labate·Gabrielle Steidl·Gerd Teschke·Stefano Vigogna
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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 $\mathcal T$ of functions on $G$, which generalizes the classical choice $\mathcal T=L_w^1(G)$. Our basic example is $ \mathcal T=\bigcap_{p\in(1,+\infty)} L^p(G)$, 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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Stephan Dahlke, Filippo De Mari, Ernesto De Vito, Demetrio Labate, Gabrielle Steidl, Gerd Teschke, Stefano Vigogna. 2014-02-17. Coorbit spaces with voice in a Fréchet space. https://arxiv.org/abs/1402.3917

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