Title : ( φ-FRAMES AND φ-RIESZ BASES ON LOCALLY COMPACT ABELIAN GROUPS )
Authors: Reihaneh Raisi Tousi , Rajab Ali Kamyabi Gol ,
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Abstract
We introduce φ-frames in L2(G), as a generalization of a- frames de ned in [8], where G is a locally compact Abelian group and φ is a topological automorphism on G. We give a characterization of φ- frames with regard to usual frames in L2(G) and show that φ-frames share several useful properties with frames. We de ne the associated φ-analysis and φ-preframe operators, with which we obtain criteria for a sequence to be a φ-frame or a φ-Bessel sequence. We also de ne φ-Riesz bases in L2(G) and establish equivalent conditions for a sequence in L2(G) to be a φ-Riesz basis.
Keywords
, φ-bracket product, φ-factorable operator, φ-frame, φ-Riesz basis, locally compact Abelian group.
@article{paperid:1023292,
author = {Raisi Tousi, Reihaneh and Kamyabi Gol, Rajab Ali},
title = {φ-FRAMES AND φ-RIESZ BASES ON LOCALLY COMPACT ABELIAN GROUPS},
journal = {Journal of the Korean Mathematical Society},
year = {2011},
volume = {48},
number = {5},
month = {January},
issn = {0304-9914},
pages = {899--912},
numpages = {13},
keywords = {φ-bracket product; φ-factorable operator; φ-frame; φ-Riesz basis;
locally compact Abelian group.},
}
%0 Journal Article
%T φ-FRAMES AND φ-RIESZ BASES ON LOCALLY COMPACT ABELIAN GROUPS
%A Raisi Tousi, Reihaneh
%A Kamyabi Gol, Rajab Ali
%J Journal of the Korean Mathematical Society
%@ 0304-9914
%D 2011
