On Limits of Multivariate B-Splines.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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B-splines occupy a pivotal position in the theory of univariate spline functions. They offer a firm bases for many of the attractive theoretical and practical properties of splines. Therefore any advance in our knowledge concerning the multivariate B-spline should be of some value. The purpose of this paper is to investigate another aspects of multivariate B-splines. We succeed in identifying those distribution functions which are limits of multivariate B-splines Polya distributions. This question was solved in one dimension by Curry and Schoenberg. Some properties of Polya distributions on Rs are also discussed.
- Statistics and Probability