Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
8
10.61186/ijmsi
14
8888
13
en
jalali
1390
8
1
gregorian
2011
11
1
6
2
online
1
fulltext
en
Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups
عمومى
General
پژوهشي
Research paper
<p>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.</p>
locally compact abelian group, shift invariant space, frame, range function, shift preserving operator, range operator.
21
32
http://ijmsi.ir/browse.php?a_code=A-10-1-96&slc_lang=en&sid=1
R.
Raisi Tousi
10031947532846002170
10031947532846002170
Yes
R.A.
Kamyabi Gol
10031947532846002171
10031947532846002171
No