Quasi-Interpolation in Shift Invariant Spaces
نویسندگان
چکیده
منابع مشابه
Quasi-interpolation in shift invariant spaces
Let s ≥ 1 be an integer, φ : Rs → R be a compactly supported function, and S(φ) denote the linear span of {φ(· − k) : k ∈ Zs}. We consider the problem of approximating a continuous function f : Rs → R on compact subsets of Rs from the classes S(φ(h·)), h > 0, based on samples of the function at scattered sites in R s. We demonstrate how classical polynomial inequalities lead to the construction...
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ABSTRACT. We discuss relations between uniform minimality, unconditionality and interpolation for families of reproducing kernels in backward shift invariant subspaces. This class of spaces contains as prominent examples the Paley-Wiener spaces for which it is known that uniform minimality does in general neither imply interpolation nor unconditionality. Hence, contrarily to the situation of st...
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Under certain assumptions on the compactly supported function 2 C(R), we propose two methods of selecting a function s from the scaled principal shift-invariant space S( ) such that s interpolates a given function f at a scattered set of data locations. For both methods, the selection scheme amounts to solving a quadratic programming problem and we are able to prove errror estimates similar to ...
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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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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2000
ISSN: 0022-247X
DOI: 10.1006/jmaa.2000.7051