Random Sampling of Mellin Band-limited Signals

2023/05/24 by Shivam Bajpeyi, Bajpeyi, Shivam, Dhiraj Patel +2
Medicine · #Cell Adhesion Molecules Research #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2305.15112

openalex publication_date 2023/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we address the random sampling problem for the class of Mellin band-limited functions BT which is concentrated on a bounded cube. It is established that any function in BT can be approximated by an element in a finite-dimensional subspace of BT. Utilizing the notion of covering number and Bernstein's inequality to the sum of independent random variables, we prove that the random sampling inequality holds with an overwhelming probability provided the sampling size is large enough.

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