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

被引：3

作者：

Tabatabaie, Seyyed Mohammad ^{[1
]}

Kazarian, Kazaros ^{[2
]}

Gol, Rajab Ali Kamyabi ^{[3
]}

Jokar, Soheila ^{[1
]}

机构：

[1] Univ Qom, Dept Math, Qom, Iran

[2] Univ Autonoma Madrid, Dept Matemat, Madrid 28049, Spain

[3] Ferdowsi Univ Mashhad, Dept Math, Mashhad, Razavi Khorasan, Iran

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2021年 / 18卷 / 01期

关键词：

Locally compact groups; Fourier transform; shift-invariant subspaces; summation basis; SPACES; TRANSLATION;

D O I：

10.1007/s00009-020-01677-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we characterize finitely generated shift-invariant subspaces of L-2(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.

引用

页数：12

共 16 条

[1]

Bloom W., 1995, Harmonic Analysis of Probability Measures on Hypergroups, V20, DOI [10.1515/9783110877595, DOI 10.1515/9783110877595]

[2] The structure of shift-invariant subspaces of L2(Rn) [J].