Osaka Journal of Mathematics

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

Raj Kumar and Ashok K. SAH

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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 $b$.

Article information

Source
Osaka J. Math. Volume 54, Number 4 (2017), 789-799.

Dates
First available in Project Euclid: 20 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1508486580

Zentralblatt MATH identifier
06821138

Subjects
Primary: 42C15: General harmonic expansions, frames
Secondary: 42C30: Completeness of sets of functions 42B35: Function spaces arising in harmonic analysis

Citation

Kumar, Raj; SAH, Ashok K. Perturbation of irregular Weyl-Heisenberg wave packet frames in $L^2(\mathbb{R})$. Osaka J. Math. 54 (2017), no. 4, 789--799.https://projecteuclid.org/euclid.ojm/1508486580


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