Mediterranean Journal of Mathematics, Volume (18), No (1), Year (2021-1)

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 ,
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Abstract

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