Discrete frames of non-uniform shifts in frequency domain

2025/08/01 by Hari Krishan Malhotra, Malhotra, Hari Krishan, Manisha Chhillar +3
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2508.00389

openalex publication_date 2025/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Dynamical sampling
• Multivariate Wavelet Frames
• Continuous and Discrete Wavelet Transforms

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