利用方向的有限集的Steiner对称化
Steiner symmetrization using a finite set of directions
摘要：
设$v_1, ..., v_m$是$\RR^n$中单位向量的有限集.假设将Steiner对称化的无穷序列应用于$\RR^n$中的紧凸集$K$，其中每个对称化都是关于$v_i$中的方向进行的。那么，由此得到的斯坦纳代数序列总是收敛的，并且极限体在序列中无限频繁出现的任何方向$v_i$上的反射下都是对称的。特别地，Steiner对称化的无限周期序列总是收敛的，并且由这个无限过程确定的集泛函总是幂等的。
英文摘要：
Let $v_1, ..., v_m$ be a finite set of unit vectors in $\RR^n$. Suppose that an infinite sequence of Steiner symmetrizations are applied to a compact convex set $K$ in $\RR^n$, where each of the symmetrizations is taken with respect to a direction from among the $v_i$. Then the resulting sequence of Steiner symmetrals always converges, and the limiting body is symmetric under reflection in any of the directions $v_i$ that appear infinitely often in the sequence. In particular, an infinite periodic sequence of Steiner symmetrizations always converges, and the set functional determined by this infinite process is always idempotent.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
