Title : ( CHARACTERIZATIONS OF SHIFT INVARIANT SPACES )
Authors: Reihaneh Raisi Tousi , Rajab Ali Kamyabi Gol ,
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Abstract
We investigate shift invariant subspaces of L2(G), where G is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group G we prove a useful Hilbert space isomorphism, introduce range functions and give a characterization of shift invariant subspaces of L2(G) in terms of range functions.
Keywords
, locally compact abelian group, shift invariant space, frame, range function
@inproceedings{paperid:1020767,
author = {Raisi Tousi, Reihaneh and Kamyabi Gol, Rajab Ali},
title = {CHARACTERIZATIONS OF SHIFT INVARIANT SPACES},
booktitle = {41th Iranian International Conference on Mathematics},
year = {2010},
location = {ارومیه, IRAN},
keywords = {locally compact abelian group; shift invariant space;
frame; range function},
}
%0 Conference Proceedings
%T CHARACTERIZATIONS OF SHIFT INVARIANT SPACES
%A Raisi Tousi, Reihaneh
%A Kamyabi Gol, Rajab Ali
%J 41th Iranian International Conference on Mathematics
%D 2010
