Coorbit spaces with voice in a Fr\'echet space
Stephan Dahlke, Filippo De Mari, Ernesto De Vito, Demetrio Labate,, Gabrielle Steidl, Gerd Teschke, Stefano Vigogna

TL;DR
This paper develops a new coorbit space theory for group representations using a Fréchet space of functions, broadening the scope beyond classical integrable cases and enabling analysis of spaces like Paley-Wiener and Shannon wavelet-related coorbit spaces.
Contribution
It introduces a general framework for coorbit spaces with kernels in a Fréchet space, extending classical theory to non-irreducible and non-integrable representations.
Findings
Allows treatment of Paley-Wiener spaces
Enables analysis of Shannon wavelets and Schr"odingerlets
Generalizes classical coorbit space theory
Abstract
We set up a new general coorbit space theory for reproducing representations of a locally compact second countable group that are not necessarily irreducible nor integrable. Our basic assumption is that the kernel associated with the voice transform belongs to a Fr\'echet space of functions on , which generalizes the classical choice . Our basic example is , 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 Schr\"odingerlets.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Seismic Imaging and Inversion Techniques · Medical Imaging Techniques and Applications
