Dual Affine invariant points
Dual Affine invariant points
复制标题
对偶仿射不变点
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
E. Werner
中科院分区：
文献类型：
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作者：
M. Meyer;C. Schuett;E. Werner
赋Hausdorff度量的R^n中凸体类上的仿射不变点是一对一仿射变换下不变的连续映射p，即p(A(K))=A(p(K)).
本文用公式Q(K^{p(K)})=p(K)对每个凸体K定义了仿射不变点p的对偶仿射点q的新概念，其中K^{p(K)}表示K关于p(K)的极.
我们研究了哪些仿射不变点确实有对偶点，这个对偶点是否是唯一的，以及它本身是否有对偶点。我们在仿射不变点集上定义了一个与对偶有关的乘积。
最后给出的例子展示了仿射不变点集的丰富结构。
An affine invariant point on the class of convex bodies in R^n, endowed with the Hausdorff metric, is a continuous map p which is invariant under one-to-one affine transformations A on R^n, that is, p(A(K))=A(p(K)).
We define here the new notion of dual affine point q of an affine invariant point p by the formula q(K^{p(K)})=p(K) for every convex body K, where K^{p(K)} denotes the polar of K with respect to p(K).
We investigate which affine invariant points do have a dual point, whether this dual point is unique and has itself a dual point. We define a product on the set of affine invariant points, in relation with duality.
Finally, examples are given which exhibit the rich structure of the set of affine invariant points.