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武汉大学学报 英文版 | Wuhan University Journal of Natural Sciences
Wan Fang
Wuhan University
Latest Article
Valuation Characteristics of Linear Transformations on R2
WANG Zhenxin, GUO Qi
Department of Mathematics, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, China
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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