%0 Journal Article
%A Raisi Tousi, R.
%A Kamyabi Gol, R.A.
%T Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups
%J Iranian Journal of Mathematical Sciences and Informatics
%V 6
%N 2
%U http://ijmsi.ir/article-1-234-en.html
%R 10.7508/ijmsi.2011.02.003
%D 2011
%K locally compact abelian group, shift invariant space, frame, range function, shift preserving operator, range operator.,
%X 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.
%> http://ijmsi.ir/article-1-234-en.pdf
%P 21-32
%& 21
%!
%9 Research paper
%L A-10-1-96
%+
%G eng
%@ 1735-4463
%[ 2011