Title : ( A RANGE FUNCTION APPROACH TO SHIFT-INVARIANT SPACES ON LOCALLY COMPACT ABELIAN GROUPS )
Authors: Rajab Ali Kamyabi Gol , Reihaneh Raisi Tousi ,
Full TextAbstract
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 familly.
@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 = {08},
number = {1},
month = {January},
issn = {0219-6913},
pages = {49--59},
numpages = {10},
keywords = {second countable locally compact groups; abelian groups; shift-invariant space; range function; frame; Riesz familly.},
}
%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
