2007/02/21 by Joseph Cima, Joseph A. Cima, Ian Graham +8
Mathematics · #32M99 #46C05 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions #math.CV #msc:32M99 #msc:46C05
paper · pdf · doi:10.48550/arxiv.math/0702620
arxiv created 2007/02/21 · openalex publication_date 2007/02/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper treats a holomorphic self-mapping f: Omega --> Omega of a bounded domain Omega in a separable Hilbert space H with a fixed point p. In case the domain is convex, we prove an infinite-dimensional version of the Cartan-Caratheodory-Kaup-Wu Theorem. This is basically a rigidity result in the vein of the uniqueness part of the classical Schwarz lemma. The main technique, inspired by an old idea of H. Cartan, is iteration of the mapping f and its derivative. A normality result for holomorphic mappings in the compact-weak-open topology, due to Kim and Krantz, is used.