Abstract
A Fourier analysis approach is taken to investigate the approximation order of scaled versions of certain linear operators into shift-invariant subspaces ofL 2(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 theL 2-approximation order of a closed shift-invariant subspace can often be realized by such an operator.
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Communicated by Carl de Boor.
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Jetter, K., Zhou, DX. Order of linear approximation from shift-invariant spaces. Constr. Approx 11, 423–438 (1995). https://doi.org/10.1007/BF01208430
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DOI: https://doi.org/10.1007/BF01208430