Abstract
We generalize the notion of B-spline to the thin plate splines and to otherd-dimensional polyharmonic splines as defined in [Duchon, [3]]; for regular nets, we give the main properties of these “B-splines”: Fourier transform, decay when ∥x∥ → ∞, stability, integration property, links between B-splines of different orders or of different dimensions and in particular link with the polynomial B-splines, approximation using B-splines... We show that, in some sense, B-splines may be considered as a regularized form of the Dirac distribution.
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Communicated by C. Brezinski
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Rabut, C. Elementarym-harmonic cardinal B-splines. Numer Algor 2, 39–61 (1992). https://doi.org/10.1007/BF02142205
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DOI: https://doi.org/10.1007/BF02142205