@ARTICLE{Raisi Tousi,
author = {Raisi Tousi, R. and Kamyabi Gol, R.A. and },
title = {Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups},
volume = {6},
number = {2},
abstract ={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. },
URL = {http://ijmsi.ir/article-1-234-en.html},
eprint = {http://ijmsi.ir/article-1-234-en.pdf},
journal = {Iranian Journal of Mathematical Sciences and Informatics},
doi = {10.7508/ijmsi.2011.02.003},
year = {2011}
}