单位球面S^(n-1)上球凸集的分析研究方法（英文）  

ANALYTIC APPROACH TO SPHERICALLY CONVEX SETS IN S^(n-1)

作　　者：邵煜骋 国起[1] SHAO Yu-cheng;GUO Qi(Department of Mathematics,Suzhou University of Science and Technology,Suzhou 215009,China)

机构地区：[1]苏州科技大学数学系,江苏苏州215009

出　　处：《数学杂志》2018年第3期473-480,共8页Journal of Mathematics

基　　金：Supported by the National Natural Science Foundation of China(11671293;11271282)

摘　　要：本文研究了欧式空间单位球面S^(n-1)上秋凸集的定义与基本性质.利用径向函数,定义了空间中有限个点的凸组合运算,并由此给出了S^(n-1)上球凸集的分析定义和集合球凸包的定义.讨论了球凸集和球凸包的基础性质.最后证明了任一闭球凸集都可以表示为其端点集的球凸包.这个结论的形成与获证完全得益于本文采用的分析方法.This article concerns with the definition and elementary properties of spherically convex sets in the Euclidean unit sphere S^（n-1）. First, we define the spherically convex combination of finitely many elements in the Euclidean spaces, in terms of which the spherically convex set and the spherically convex hull of sets in S^（n-1） are defined, then study the properties of the spherically convex sets and hulls. Finally, we prove that each closed spherically convex set can be expressed as the spherically convex hull of its extreme point set, the formulation and proof of which benifit from the analytic approach adopted in this paper.

关 键 词：球面凸集 球面凸组合 径向函数 凸包 锥包 

分 类 号：O184[理学—数学] O177.99[理学—基础数学]