On the structure of finitely generated shift-invariant subspaces
Classical Analysis and ODEs
2019-06-18 v2
Abstract
A characterization of finitely generated shift-invariant subspaces is given when generators are g-minimal. An algorithm is given for the determination of the coefficients in the well known representation of the Fourier transform of an element of the finitely generated shift-invariant subspace as a linear combination of Fourier transformations of generators. An estimate for the norms of those coefficients is derived. For the proof a sort of orthogonalization procedure for generators is used which reminds the well known Gram-Schmidt orthogonalization process.
Cite
@article{arxiv.1605.02456,
title = {On the structure of finitely generated shift-invariant subspaces},
author = {K. S. Kazarian},
journal= {arXiv preprint arXiv:1605.02456},
year = {2019}
}