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Some recurrence formulas for box splines and cone splines

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Analysis in Theory and Applications

Abstract

A degree elevation formula for multivariate simplex splines was given by Micchelli [6] and extended to hold for multivariate Dirichlet splines in [8]. We report similar formulae for multivariate cone splines and box splines. To this end, we utilize a relation due to Dahmen and Micchelli [4] that connects box splines and cone splines and a degree reduction formula given by Cohen, Lyche, and Riesenfeld in [2].

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Authors and Affiliations

  1. Department of Mathematics, University of st. Thomas, 55105, St. Paul, MN, USA

    Patrick J. Van Fleet

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  1. Patrick J. Van Fleet
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Correspondence to Patrick J. Van Fleet.

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Van Fleet, P.J. Some recurrence formulas for box splines and cone splines. Approx. Theory & its Appl. 18, 81–89 (2002). https://doi.org/10.1007/BF02837050

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  • DOI: https://doi.org/10.1007/BF02837050

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