Frames With Several Generators Associated with Weyl-Heisenberg Group and Extended Affine Group
arXiv:2112.06037 · doi:10.1007/s40840-022-01337-6
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.