Discrete frames of non-uniform shifts in frequency domain
Functional Analysis
2025-08-04 v1
Abstract
Frames in separable Hilbert spaces gives stable analysis and reconstruction of each vector in the underlying space. In this paper, we study frame conditions for a collection of matrix-valued functions obtained by non-uniform shifts. We give necessary and sufficient conditions for the existence of matrix-valued discrete Bessel sequence over non-uniform displacement parameters in terms of the Fourier transform of window functions. We also present perturbation results for matrix-valued non-uniform discrete frames.
Keywords
Cite
@article{arxiv.2508.00389,
title = {Discrete frames of non-uniform shifts in frequency domain},
author = {Hari Krishan Malhotra and Manisha Chhillar and Lalit Kumar Vashisht},
journal= {arXiv preprint arXiv:2508.00389},
year = {2025}
}