极体算子与M-加算子的极表示

doi:10.12066/j.issn.1007-2861.2092

上海大学学报(自然科学版) ›› 2020, Vol. 26 ›› Issue (5): 834-841.doi: 10.12066/j.issn.1007-2861.2092

极体算子与M-加算子的极表示

刘畅, 冷岗松()

上海大学理学院, 上海 200444

收稿日期:2018-08-29 出版日期:2020-10-30 发布日期:2020-01-10
通讯作者: 冷岗松 E-mail:gleng@staff.shu.edu.cn
基金资助:
国家自然科学基金资助项目(11671249)

Extremal representations of polar set and ${M}$-addition

LIU Chang, LENG Gangsong()

College of Sciences, Shanghai University, Shanghai 200444, China

Received:2018-08-29 Online:2020-10-30 Published:2020-01-10
Contact: LENG Gangsong E-mail:gleng@staff.shu.edu.cn

摘要/Abstract

摘要：

研究了极体算子和 M-加算子的极表示. 对于 Rⁿ中的紧凸集 K, 证明了 K° = (ext K)°. 证明了当 K,L 为 Rⁿ 中包含原点的凸体, M 为 R² 中第一象限中的凸体时, 有 K 和 L 的 M-加等于 K 和 L 的 (bdM)-加. 通过举出反例, 说明当 M 不在第一象限或者 K, L 不包括原点时, 二者不一定相等.

关键词: 凸几何, 极体, M-加, 极表示

Abstract:

The extremal representations of the polar set and M-addition are studied. If K is a compact and convex subset of Rⁿ, then we have K° = (ext K)°. It is proved that M-sum of K and L is equal to the (bd M)-sum, if K and $L$ are convex bodies containing the origin and M is a convex body in the first quadrant of R². Moreover, by the counter-examples given in section 3, all these conditions cannot be removed.

Key words: convex geometry, polar set, $M$-addition, extremal representations

中图分类号:

O186

刘畅, 冷岗松. 极体算子与M-加算子的极表示[J]. 上海大学学报(自然科学版), 2020, 26(5): 834-841.

LIU Chang, LENG Gangsong. Extremal representations of polar set and ${M}$-addition[J]. Journal of Shanghai University（Natural Science Edition）, 2020, 26(5): 834-841.

图/表 2

参考文献 10

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极体算子与M-加算子的极表示

Extremal representations of polar set and ${M}$-addition

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