Random sampling in reproducing kernel subspaces of Lp (Rn)

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:491

Article

Patel, Dhiraj¹  Sampath, Sivananthan¹ 

[1] Indian Inst Technol Delhi, Dept Math, New Delhi 110016, India

关键词: Idempotent operator;    Reproducing kernel space;    Random sampling;    p-frame;    Reconstruction algorithm;   

DOI  :  10.1016/j.jmaa.2020.124270

来源: Elsevier

【 摘 要 】

In this paper, we study random sampling in a reproducing kernel space V, which is the range of an idempotent integral operator. Under certain decay condition on the integral kernel, we show that any element in V can be approximated by an element in a finite-dimensional subspace of V. Moreover, we prove with overwhelming probability that random points uniformly distributed over a cube C is a stable set of sampling for the set of functions concentrated on C. Further, we discuss a reconstruction algorithm for functions in a finite-dimensional subspace of V from its random samples. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free