Continuous Wavelet Frames on the Sphere: The Group-Theoretic Approach Revisited
Functional Analysis
2024-07-11 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2012.13460,
title = {Continuous Wavelet Frames on the Sphere: The Group-Theoretic Approach Revisited},
author = {S. Dahlke and F. De Mari and E. De Vito and M. Hansen and M. Hasannasab and M. Quellmalz and G. Steidl and G. Teschke},
journal= {arXiv preprint arXiv:2012.13460},
year = {2024}
}