Iranian Journal of Mathematical Sciences and Informatics, Volume (6), No (2), Year (2011-7) , Pages (1-17)

Title : ( Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups )

Authors: Reihaneh Raisi Tousi , Rajab Ali Kamyabi Gol ,

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We investigate shift invariant subspaces of $L^2(G)$, 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 $L^2(G)$ in terms of range functions. Finally, we investigate shift preserving operators on locally compact abelian groups. We show that there is a one-to-one correspondence between shift preserving operators and range operators on $L^2(G)$ where $G$ is a locally compact abelian group.

Keywords

, locally compact abelian group, shift invariant space, frame, range function, shift preserving operator, range
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@article{paperid:1022717,
author = {Raisi Tousi, Reihaneh and Kamyabi Gol, Rajab Ali},
title = {Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups},
journal = {Iranian Journal of Mathematical Sciences and Informatics},
year = {2011},
volume = {6},
number = {2},
month = {July},
issn = {1735-4463},
pages = {1--17},
numpages = {16},
keywords = {locally compact abelian group; shift invariant space; frame; range function; shift preserving operator; range operator},
}

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%0 Journal Article
%T Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups
%A Raisi Tousi, Reihaneh
%A Kamyabi Gol, Rajab Ali
%J Iranian Journal of Mathematical Sciences and Informatics
%@ 1735-4463
%D 2011

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