Approximation from locally finite-dimensional shift-invariant spaces
نویسندگان
چکیده
منابع مشابه
Locally Finite Dimensional Shift-invariant Spaces in R
We prove that a locally finite dimensional shift-invariant linear space of distributions must be a linear subspace of some shift-invariant space generated by finitely many compactly supported distributions. If the locally finite dimensional shift-invariant space is a subspace of the Hölder continuous space C or the fractional Sobolev space L , then the superspace can be chosen to be C or L , re...
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متن کاملLocally Finitely Dimensional Shift-invariant Spaces in R
We prove that a locally finitely dimensional shiftinvariant linear space of distributions must be a linear subspace of some shift-invariant space generated by finitely many compactly supported distributions. If the locally finitely dimensional shiftinvariant space is a subspace of the Hölder continuous space C or the fractional Sobolev space L , then the superspace can be chosen to be C or L , ...
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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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Approximation orders of shift-invariant subspaces of L p (IR d), 2 p 1, generated by the shifts of one compactly supported function are considered. In that course, explicit approximation maps are constructed. The approach avoids quasi-interpolation and applies to stationary and non-stationary reenements. The general results are specialized to box spline spaces, to obtain new results on their ap...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1996
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-96-03253-4