Similarity of holomorphic matrices

Abstract

AbstractLet Ω be a noncompact Riemann surface (e.g., the complex plane). The main result is that if A and B are two square holomorphic matrices on Ω such that for any z in Ω, there is a neighborhood of z with A and B holomorphically similar on the neighborhood, then A and B are holomorphically similar on Ω. This is then applied to extend results of Wasow on pointwise similarity. We actually prove these results for Bezout domains satisfying certain conditions, and then observe that these conditions are satisfied by the ring of holomorphic functions on Ω