论文标题
关于仿射图的家族的广义凸度
Generalised convexity with respect to families of affine maps
论文作者
论文摘要
集合的标准凸封面船体定义为所有图像的交点，在一组刚性运动的作用下，包含给定集的半空间。在本文中，我们提出了这个经典概念的概括，即我们称为$（k，\ mathbb {h}）$ - 船体，并通过上述构造获得了上述构造获得的，它可以用其他凸面的euclidean空间的近距离$ k $替换为euclidean空间的近距离子集$ k $，并由子集$ \ nater $ \ mathbb c y}组成的一组僵化的动议。主要重点是对$（K，\ Mathbb {h}）$的分析 - 从$ k $中的随机样品凸出。
The standard convex closed hull of a set is defined as the intersection of all images, under the action of a group of rigid motions, of a half-space containing the given set. In this paper we propose a generalisation of this classical notion, that we call a $(K,\mathbb{H})$-hull, and which is obtained from the above construction by replacing a half-space with some other convex closed subset $K$ of the Euclidean space, and a group of rigid motions by a subset $\mathbb{H}$ of the group of invertible affine transformations. The main focus is put on the analysis of $(K,\mathbb{H})$-convex hulls of random samples from $K$.
