Perturbation of irregular Weyl-Heisenberg wave packet frames in $L^2(\mathbb{R})$

Abstract

In this paper, we consider the perturbation problem of irregular Weyl-Heisenberg wave packet frame $\{D_{a_j}T_{bk}E_{c_m}\psi\}_{j,k,m\in \mathbb{Z}}$ about dilation, translation and modulation parameters. We give a method to determine whether the perturbation systems is a frame for wave packet functions whose Fourier transforms have small support and prove the stability about dilation parameter on Paley-Wiener space. For a wave packet function, we give a definite answer to the stability about translation parameter $b$.