Random sampling and reconstruction in reproducing kernel subspace of mixed Lebesgue spaces

In this article, we consider the random sampling in the image space of an idempotent integral operator on mixed Lebesgue space . We assume some decay and regularity conditions on the integral kernel and show that the bounded functions in can be approximated by an element in a finite‐dimensional subspace of on . Consequently, we show that the set of bounded functions concentrated on is totally bounded and prove with an overwhelming probability that the random sample set uniformly distributed over is a stable set of sampling for the set of concentrated functions on . Further, we propose an iterative scheme to reconstruct the concentrated functions from their random measurements.