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arXiv · 2508.00389

Discrete frames of non-uniform shifts in frequency domain

Hari Krishan Malhotra·Manisha Chhillar·Lalit Kumar Vashisht
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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.

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Hari Krishan Malhotra, Manisha Chhillar, Lalit Kumar Vashisht. 2025-08-01. Discrete frames of non-uniform shifts in frequency domain. https://arxiv.org/abs/2508.00389

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