AU - Raisi Tousi, R.
AU - Kamyabi Gol, R.A.
TI - Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups
PT - JOURNAL ARTICLE
TA - IJMSI
JN - IJMSI
VO - 6
VI - 2
IP - 2
4099 - http://ijmsi.ir/article-1-234-en.html
4100 - http://ijmsi.ir/article-1-234-en.pdf
SO - IJMSI 2
ABĀ - 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.
CP - IRAN
IN -
LG - eng
PB - IJMSI
PG - 21
PT - Research paper
YR - 2011