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Order of linear approximation from shift-invariant spaces. (English) Zbl 0840.41025

Summary: A Fourier analysis approach is taken to investigate the approximation order of scaled versions of certain linear operators into shift-invariant subspaces of \(L_2 (\mathbb{R}^d)\). Quasi-interpolants and cardinal interpolants are special operators of this type, and we give a complete characterization of the order in terms of some type of ellipticity condition for a related function. We apply these results by showing that the \(L_2\)-approximation order of a closed shift-invariant subspace can often be realized by such an operator.

MSC:

41A63 Multidimensional problems
41A25 Rate of convergence, degree of approximation
65D10 Numerical smoothing, curve fitting
Full Text: DOI

References:

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