Relevant sampling in a reproducing kernel subspace of Orlicz space

In this paper, we aim to provide a general paradigm for dealing with the sampling and random sampling problem in a reproducing kernel subspace of Orlicz space Formula: see text. We consider the function space Formula: see text as the image of an idempotent integral operator on Formula: see text, where the integral kernel satisfies certain off-diagonal decay and regularity conditions. The model example of such reproducing kernel subspace of Formula: see text includes the finitely generated shift-invariant space and signal space with a finite rate of innovation. We show that a signal in Formula: see text can be stably reconstructed from its samples at distinct points separated by a sufficiently small gap. Next, we deduce that the random sampling inequality holds with a high probability for the class of functions in Formula: see text concentrated on a cube Formula: see text, when the samples collected at i.i.d. random points are drawn on Formula: see text of order Formula: see text.