Open AccessThe random convolution sampling stability in multiply generated shift invariant subspace of weighted mixed Lebesgue space
Author(s) -
Suping Wang
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022098
Subject(s) - mathematics , convolution (computer science) , subspace topology , invariant (physics) , invariant subspace , standard probability space , lebesgue integration , sampling (signal processing) , linear subspace , stability (learning theory) , mathematical analysis , pure mathematics , discrete mathematics , physics , computer science , artificial intelligence , machine learning , detector , artificial neural network , optics , mathematical physics
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.