Random sampling in reproducing kernel subspaces of [formula omitted

Abstract

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.