On Coorbit Fr\'echet Spaces
Functional Analysis
2025-12-22 v1
Abstract
This paper is concerned with a new approach to coorbit space theory. Usually, coorbit spaces are defined by collecting all distributions for which the voice transform associated with a square-integrable group representation possesses a certain decay, usually measured in a Banach space norm such as weighted -norms. Unfortunately, in cases where the representation does not satisfy certain integrability conditions, one is faced with a bottleneck, namely that the discretization of the coorbit spaces is surprisingly difficult. It turns out that in these cases the construction of coorbit spaces as Fr\'echet spaces is much more convenient since then atomic decompositions can be established in a very natural way.
Cite
@article{arxiv.2512.17502,
title = {On Coorbit Fr\'echet Spaces},
author = {S. Dahlke and F. De Mari and E. De Vito and M. Hansen and G. Steidl and G. Teschke},
journal= {arXiv preprint arXiv:2512.17502},
year = {2025}
}