On limits of multivariateB-splines

Abstract : 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.