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High levelm-harmonic cardinal B-splines

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Abstract

We generalize the notion ofm-harmonic cardinal B-spline defined in [Rabut, [6c]] to obtain “B-splines” on an infinite regular grid, which are halfway between “elementary B-splines” and the Lagrangean cardinal spline function. We give the main properties of these functions: Fourier transform, decay when ∥x∥ → ∞, integration,P k -reproduction (fork<-2m−1) of the associated B-spline approximation, etc. We show that, in some sense, “high levelm-harmonic B-splines” may be considered as a finer regular approximation of the Dirac distribution than the elementarym-harmonic B-splines are.

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Authors and Affiliations

  1. Complexe scientifique de Rangueil, INSA, Centre de Mathématiques, 31077, Toulouse Cédex, France

    Christophe Rabut

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  1. Christophe Rabut
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Communicated by C. Brezinski

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Rabut, C. High levelm-harmonic cardinal B-splines. Numer Algor 2, 63–84 (1992). https://doi.org/10.1007/BF02142206

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  • DOI: https://doi.org/10.1007/BF02142206

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