Volume 6, Issue 2 (11-2011)                   IJMSI 2011, 6(2): 21-32 | Back to browse issues page

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Raisi Tousi R, Kamyabi Gol R. Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups. IJMSI. 2011; 6 (2) :21-32
URL: http://ijmsi.ir/article-1-234-en.html

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.

Type of Study: Research paper | Subject: General

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