CONVEXITY AND BERNSTEIN POLYNOMIALS ON k-SIMPLOIDS

作     者：WOLFGANG DAHMEN CHARLES A.MICCHELLI 

作者机构：Institut fur Mathematik ⅢFreie Universitat Berlin Arnimallee 2-61000 Berlin(West)33GermanyIBM T.J.Watson Research CenterP.O.Box 218Yorktown HeightsN.Y.10598U.S.A. 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：1990年第6卷第1期

页      面：50-66页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This work was partially supported by NATO Grant No.DJ RG 639/84 

主　　题：Bernstein 多项式 凸性 

摘      要：This paper is concerned with Bernstein polynomials on k-simploids by which we mean a crossproduct of k lower dimensional simplices. Specifically, we show that if the Bernstein polynomials ofa given function f on a k-simploid form a decreasing sequence then f+l, where l is any correspondingtensor product of affine functions. achieves its maximum on the boundary of the k-simploid. Thisextends recent results in [1] for bivariate Bernstein polynomials on triangles. Unlike the approachused in [1] our approach is based on semigroup techniques and the maximum principle for secondorder elliptic operators. Furthermore, we derive analogous results for cube spline surfaces.