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武汉大学学报 英文版 | Wuhan University Journal of Natural Sciences
Wan Fang
CNKI
CSCD
Wuhan University
Latest Article
Valuation Characteristics of Linear Transformations on R2
Time:2019-11-15  
WANG Zhenxin, GUO Qi
Department of Mathematics, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, China
Abstract:
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 natu-ral 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.
Key words:Minkowski valuation; linear translation; translations; convex body
CLC number:O 184
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