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Fractional cone and hex splines. (English) Zbl 1375.41005

In this paper the authors study the mathematical foundations of cone and hex splines of fractional and complex orders. These two spline families generalize the univariate concepts of fractional and complex B-splines. This approach is based on a generalized version of the Hermite-Genocchi formula and produces the analog of multivariate simplex splines (of complex orders). The focus of their setting lies more on the geometry of the knot set.

MSC:

41A15 Spline approximation
65D07 Numerical computation using splines
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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