Random sampling stability in weighted reproducing kernel subspaces of
$L_\nu^p(\mathbb{R}^d)$
Abstract
In this paper, we mainly study the random sampling stability for signals
in a weighted reproducing kernel subspace of
$L_\nu^p(\mathbb{R}^d)$ without
the additional requirement that the kernel function has symmetry. The
sampling set is independently and randomly drawn from a general
probability distribution over $\mathbb{R}^d$.
Based on the frame characterization of weighted reproducing kernel
subspaces, we first approximate the weighted reproducing kernel space by
a finite dimensional subspace on any bounded domains. Then, we prove
that the random sampling stability holds with high probability for all
signals in weighted reproducing kernel subspaces whose energy
concentrate on a cube when the sampling size is large enough.