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An upper bound on the approximation power of principal shift-invariant spaces

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Abstract

An upper bound on theL p-approximation power (1 ≤p ≤ ∞) provided by principal shift-invariant spaces is derived with only very mild assumptions on the generator. It applies to both stationary and nonstationary ladders, and is shown to apply to spaces generated by (exponential) box splines, polyharmonic splines, multiquadrics, and Gauss kernel.

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  1. Department of Mathematics and Computer Science Faculty of Science, Kuwait University, P.O. Box 5969, 13060, Safat, Kuwait

    M. J. Johnson

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  1. M. J. Johnson
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Communicated by Ronald A. DeVore.

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Johnson, M.J. An upper bound on the approximation power of principal shift-invariant spaces. Constr. Approx 13, 155–176 (1997). https://doi.org/10.1007/BF02678462

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  • DOI: https://doi.org/10.1007/BF02678462

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