Workshop of Matrix Analysis, Frames and Wavelets Theory , 2010-02-02

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 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. Finally, we investigate shift preserving operators on locally compact abelian groups. We show that there is a oneto- one correspondence between shift preserving operators and range operators on L2(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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@inproceedings{paperid:1020894,
author = {Raisi Tousi, Reihaneh and Kamyabi Gol, Rajab Ali},
title = {Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups},
booktitle = {Workshop of Matrix Analysis, Frames and Wavelets Theory},
year = {2010},
location = {رفسنجان, IRAN},
keywords = {locally compact abelian group; shift invariant space; frame; range function; shift preserving operator; range operator.},
}

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%0 Conference Proceedings
%T Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups
%A Raisi Tousi, Reihaneh
%A Kamyabi Gol, Rajab Ali
%J Workshop of Matrix Analysis, Frames and Wavelets Theory
%D 2010

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