The random convolution sampling stability in multiply generated shift invariant subspace of weighted mixed Lebesgue space

In this paper, we mainly investigate the random convolution sampling stability for signals in multiply generated shift invariant subspace of weighted mixed Lebesgue space. Under some restricted conditions for the generators and the convolution function, we conclude that the defined multiply generated shift invariant subspace could be approximated by a finite dimensional subspace. Furthermore, with overwhelming probability, the random convolution sampling stability holds for signals in some subset of the defined multiply generated shift invariant subspace when the sampling size is large enough.