arXiv subjects

G. Teschke

Publications and source records attributed to G. Teschke.

2 recordsLinked to original sources

arXiv2025

On Coorbit Fr\'echet Spaces

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 $L_p$-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.

math.FA↗

arXiv2020

Continuous Wavelet Frames on the Sphere: The Group-Theoretic Approach Revisited

In \cite{AV99}, Antoine and Vandergheynst propose a group-theoretic approach to continuous wavelet frames on the sphere. The frame is constructed from a single so-called admissible function by applying the unitary operators associated to a representation of the Lorentz group, which is square-integrable modulo the nilpotent factor of the Iwasawa decomposition. We prove necessary and sufficient conditions for functions on the sphere, which ensure that the corresponding system is a frame. We strengthen a similar result in \cite{AV99} by providing a complete and detailed proof.

math.FA↗