Shift invariant spaces on compact groups
نویسندگان
چکیده
منابع مشابه
Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups
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 funct...
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Abstract— In this paper, a necessary and sufficient condition for sampling in the general framework of shift invariant spaces is derived. Then this result is applied respectively to the regular sampling and the perturbation of regular sampling in shift invariant spaces. A simple necessary and sufficient condition for regular sampling in shift invariant spaces is attained. Furthermore, an improv...
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In this correspondence, a necessary and sufficient condition for sampling in the general framework of shift-invariant spaces is derived. Then this result is applied, respectively, to the regular sampling and the perturbation of regular sampling in shift-invariant spaces. A simple necessary and sufficient condition for regular sampling in shift-invariant spaces is attained. Furthermore, an impro...
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We investigate the structure of shift-invariant spaces generated by a finite number of compactly supported functions in Lp(R) (1 ≤ p ≤ ∞). Based on a study of linear independence of the shifts of the generators, we characterize such shift-invariant spaces in terms of the semi-convolutions of the generators with sequences on Z. Moreover, we show that such a shiftinvariant space provides Lp-appro...
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ژورنال
عنوان ژورنال: Bulletin des Sciences Mathématiques
سال: 2013
ISSN: 0007-4497
DOI: 10.1016/j.bulsci.2012.11.003