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Random Sampling of Mellin Band-Limited Signals

被引：1
|
作者：
Bajpeyi, Shivam [1 ,2 ]
Patel, Dhiraj [2 ]
Sivananthan, S. [2 ]
机构：
[1] Sardar Vallabhbhai Natl Inst Technol Surat, Dept Math, Surat 395007, Gujarat, India
[2] Indian Inst Technol Delhi, Dept Math, New Delhi, India
来源：
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2024年 / 45卷 / 02期
关键词：
Mellin band-limited functions; Mellin transform; random sampling; reproducing kernel space; sampling inequality; FRACTIONAL CALCULUS; RECONSTRUCTION; FOUNDATIONS; THEOREM;
D O I：
10.1080/01630563.2024.2318576
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we address the random sampling problem for the class of functions in the space of Mellin band-limited functions BT, which are concentrated on a bounded cube. It is established that any Mellin band-limited function 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 probabilistic sampling inequality holds for the set of concentrated signals in BT with an overwhelming probability provided the sampling size is large enough.
引用
收藏
页码：136 / 150
页数：15
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