Title : ( The Structure of Finitely Generated Shift-Invariant Subspaces on Locally Compact Abelian Groups )
Authors: Seyyed Mohammad Tabatabaie , Kazaros Kazarian , Rajab Ali Kamyabi Gol , Soheila Jokar ,
Full TextAbstract
In this paper, we characterize finitely generated shift-invariant subspaces of L2(G), where G is a locally compact abelian group. In particular, we give a formula for the coefficients in the known representation of the Fourier transform of the elements of finitely generated shift-invariant subspaces. Also, certain orthogonalization procedure for generators which is reminiscent of the Gram–Schmidt orthogonalization process is given.
Keywords
, Locally compact groups, Fourier transform, shift-invariant subspaces, summation basis
@article{paperid:1087489,
author = {Seyyed Mohammad Tabatabaie and Kazaros Kazarian and Kamyabi Gol, Rajab Ali and Soheila Jokar},
title = {The Structure of Finitely Generated Shift-Invariant Subspaces on Locally Compact Abelian Groups},
journal = {Mediterranean Journal of Mathematics},
year = {2021},
volume = {18},
number = {1},
month = {January},
issn = {1660-5446},
keywords = {Locally compact groups; Fourier transform; shift-invariant
subspaces; summation basis},
}
%0 Journal Article
%T The Structure of Finitely Generated Shift-Invariant Subspaces on Locally Compact Abelian Groups
%A Seyyed Mohammad Tabatabaie
%A Kazaros Kazarian
%A Kamyabi Gol, Rajab Ali
%A Soheila Jokar
%J Mediterranean Journal of Mathematics
%@ 1660-5446
%D 2021
