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2017 Fractional cone and hex splines
Peter R. Massopust, Patrick J. Van Fleet
Rocky Mountain J. Math. 47(5): 1655-1691 (2017). DOI: 10.1216/RMJ-2017-47-5-1655

Abstract

We introduce an extension of cone splines and box splines to fractional and complex orders. These new families of multivariate splines are defined in the Fourier domain along certain $s$-directional meshes and include as special cases the $3$-directional box splines~\cite {article:condat} and hex splines~\cite {article:vandeville} previously considered by Condat and Van De Ville, et al. These cone and hex splines of fractional and complex order generalize the univariate fractional and complex B-splines defined in~\cite {article:fbu, article:ub} and, e.g., investigated in~\cite {article:fm, article:mf}. Explicit time domain representations are de\-rived for these splines on $3$-directional meshes. We present some properties of these two multivariate spline families, such as recurrence, decay and refinement. Finally, we show that a bivariate hex spline and its integer lattice translates form a Riesz basis of its linear span.

Citation

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Peter R. Massopust. Patrick J. Van Fleet. "Fractional cone and hex splines." Rocky Mountain J. Math. 47 (5) 1655 - 1691, 2017. https://doi.org/10.1216/RMJ-2017-47-5-1655

Information

Published: 2017
First available in Project Euclid: 22 September 2017

zbMATH: 1375.41005
MathSciNet: MR3705767
Digital Object Identifier: 10.1216/RMJ-2017-47-5-1655

Subjects:
Primary: 41A15 , 42A38 , 65D07

Keywords: $s$-dimensional mesh , (fractional) difference operator , box splines , Cone splines , fractional and complex B-splines , hex splines

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 5 • 2017
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