International Journal of Wavelets, Multiresolution and Information Processing, ( ISI ), Volume (8), No (1), Year (2010-3) , Pages (49-59)

Title : ( A Range Function Approach To Shift-Invariant Spaces On Locally Compact Abelian Groups )

Authors: Rajab Ali Kamyabi Gol , Reihaneh Raisi Tousi ,

Citation: BibTeX | EndNote

This paper devoted several aspects of shift-invariant spaces on locally compact abelian groups. For a second countable locally compact abelian group G we prove a useful HILBERT SPACE ISIMORPHISM,introduce range functions and give a characterization of shift-invariant subspaces of L^2(G) in terms of range functions. Utilizaing these functions, we generalize charaterizations of frames and Riesz bases generated by shifts of a countable set of generators from L2(Rn) to L2(G).

Keywords

, second countable locally compact groups, abelian groups, shift-invariant space, range function; frame, Riesz
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@article{paperid:1015402,
author = {Kamyabi Gol, Rajab Ali and Raisi Tousi, Reihaneh},
title = {A Range Function Approach To Shift-Invariant Spaces On Locally Compact Abelian Groups},
journal = {International Journal of Wavelets, Multiresolution and Information Processing},
year = {2010},
volume = {8},
number = {1},
month = {March},
issn = {0219-6913},
pages = {49--59},
numpages = {10},
keywords = {second countable locally compact groups; abelian groups; shift-invariant space; range function; frame; Riesz familly.},
}

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%0 Journal Article
%T A Range Function Approach To Shift-Invariant Spaces On Locally Compact Abelian Groups
%A Kamyabi Gol, Rajab Ali
%A Raisi Tousi, Reihaneh
%J International Journal of Wavelets, Multiresolution and Information Processing
%@ 0219-6913
%D 2010

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