Random sampling stability of signals in weighted reproducing kernel spaces

For the independent random samples obtained according to the general probability distribution, the random sampling stability of signals is studied in the weighted reproducing kernel subspace under the condition that the kernel function does not satisfy the symmetry. Firstly, based on the framework characterization of the weighted reproducing kernel subspace, the finite dimensional subspace is used to approximate the weighted reproducing kernel space on the bounded region. Secondly, by studying the relationship between the infinite norm and p norm of signals in the weighted reproducing kernel subspace, the covering number of the normalized finite dimensional subspace is estimated. Finally, it is proved that the random sampling stability of the weighted reproducing kernel signals with energy concentrated on the cube is valid with high probability when the sampling quantity is large enough.