English

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}
}