The Structure of Finitely Generated Shift-Invariant Subspaces on Locally Compact Abelian Groups

被引：0
作者：
Seyyed Mohammad Tabatabaie
Kazaros Kazarian
Rajab Ali Kamyabi Gol
Soheila Jokar
机构：
[1] University of Qom,Department of Mathematics
[2] Universidad Autonoma de Madrid,Departamento de Matematicas
[3] Ferdowsi University of Mashhad,Department of Mathematics
来源：
Mediterranean Journal of Mathematics | 2021年 / 18卷
关键词：
Locally compact groups; Fourier transform; shift-invariant subspaces; summation basis; Primary 43A15; Secondary 43A25; 46E30;
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摘要：
In this paper, we characterize finitely generated shift-invariant subspaces of L2(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2(G)$$\end{document}, 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.
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