Valuation Characteristics of Linear Transformations on R^2  

作　　者：WANG Zhenxin GUO Qi 

机构地区：[1]Department of Mathematics, Suzhou University of Science and Technology

出　　处：《Wuhan University Journal of Natural Sciences》2019年第6期485-492,共8页武汉大学学报（自然科学英文版）

基　　金：Supported by the National Natural Science Foundation of China(11671293,11271282);partially by the Research Innovation Fund of Suzhou University of Science and Technology(SKCX17 031)

摘　　要：In this paper,we study the Minkowski valuations on the set of 1 or 2 dimensional convex bodies compatible with a linear transformation and translations in some sense.We first introduce a kind of compatibility that all linear transformations(as Minkowski valuations)possess naturally.Then,we show that,under some natural conditions,monotone Minkowski valuations with such compatibility are exactly linear transformations.So we obtain a valuation characterization of linear transformations on Euclidean 1 or 2-spaces.In this paper, we study the Minkowski valuations on the set of 1 or 2 dimensional convex bodies compatible with a linear transformation and translations in some sense. We first introduce a kind of compatibility that all linear transformations(as Minkowski valuations) possess naturally. Then, we show that, under some natural conditions, monotone Minkowski valuations with such compatibility are exactly linear transformations. So we obtain a valuation characterization of linear transformations on Euclidean 1 or 2-spaces.

关 键 词：MINKOWSKI VALUATION linear TRANSLATION TRANSLATIONS CONVEX body 

分 类 号：O184[理学—数学]