椭球的Orlicz投影体(英文)  

ORLICZ PROJECTION BODIES OF ELLIPSOIDS

作　　者：王健[1] 

机构地区：[1]上海大学理学院数学系,上海200444

出　　处：《数学杂志》2014年第1期79-84,共6页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11001163);Innovation Program of Shanghai Municipal Education Commission(11YZ11);Shanghai Leading Academic Discipline Project(J50101)

摘　　要：本文研究了文献[1]所引入的Orlicz投影体问题.利用Orlicz投影体在线性变换下的不变性,获得了椭球的Orlicz投影体仍是椭球的结果.作为例子,计算了当取两个特定的凸函数时单位球的Orlicz投影体的支持函数.In this paper, we study the problem of the Orlicz projection bodies recently introduced by Lutwak, Yang and Zhang. By using the linear invariant property of Orlicz projection bodies, we obtain the result that the Orlicz projection bodies of ellipsoids are still ellipsoids. As examples, we compute two concrete support functions of Orlicz projection bodies of the unit ball for two specific convex functions.

关 键 词：凸体 支持函数 投影体 Orlicz投影体 

分 类 号：O186.5[理学—数学]