论文标题
身份操作员和近端映射的根：（经典和幻影）循环和间隙向量
Roots of the identity operator and proximal mappings: (classical and phantom) cycles and gap vectors
论文作者
论文摘要
最近，西蒙斯（Simons）为希尔伯特（Hilbert）空间中的封闭凸的支撑功能提供了引理，并用它证明了投影周期上的几何猜想。在本文中，我们将Simons的引理扩展到封闭的凸功能，显示其与Attouch-Thera二元性的连接，并使用它来表征近端映射的（经典和幻影）周期和间隙向量。
Recently, Simons provided a lemma for a support function of a closed convex set in a general Hilbert space and used it to prove the geometry conjecture on cycles of projections. In this paper, we extend Simons's lemma to closed convex functions, show its connections to Attouch-Thera duality, and use it to characterize (classical and phantom) cycles and gap vectors of proximal mappings.
