Abstract
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.
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