Frames With Several Generators Associated with Weyl-Heisenberg Group and Extended Affine Group
Functional Analysis
2022-08-02 v2
Abstract
We study the construction of Gabor frames and wavelet frames for Weyl-Heisenberg group and extended affine group by using contraction between the affine group and the Weyl-Heisenberg group due to Subag, Baruch, Birman and Mann. Firstly, we give construction of Gabor frames with several generators from a unitary irreducible representation associated to the Weyl-Heisenberg group. Wavelet frames with several generators associated with an extended affine group have been obtained. A relation between frames for Weyl-Heisenberg group and extended affine group is also discussed. Finally, we show that frames of Gabor and wavelet structure are stable under small perturbations.
Keywords
Cite
@article{arxiv.2112.06037,
title = {Frames With Several Generators Associated with Weyl-Heisenberg Group and Extended Affine Group},
author = {Divya Jindal and Lalit Kumar Vashisht},
journal= {arXiv preprint arXiv:2112.06037},
year = {2022}
}