论文标题
凸组的差异向量和几何猜想的分辨率
The difference vectors for convex sets and a resolution of the geometry conjecture
论文作者
论文摘要
几何猜想是在将近四分之一世纪前提出的，它指出，投影仪的固定点集合在希尔伯特（Hilbert）空间中的非空封闭凸组上的固定点集实际上等于基础集合的某些翻译的交点。 在本文中，我们提供了几何猜想的完整分辨率。我们的证明依赖于单调操作员理论。我们重新访问了以前已知的结果，并提供了各种说明性示例。还介绍了有关涉及数量的数值计算的评论。
The geometry conjecture, which was posed nearly a quarter of a century ago, states that the fixed point set of the composition of projectors onto nonempty closed convex sets in Hilbert space is actually equal to the intersection of certain translations of the underlying sets. In this paper, we provide a complete resolution of the geometry conjecture. Our proof relies on monotone operator theory. We revisit previously known results and provide various illustrative examples. Comments on the numerical computation of the quantities involved are also presented.
