Separation of Boundary Singularities for Holomorphic Generators

2010/02/25 by Mark Elin, Elin, Mark, David Shoikhet +3
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1002.4883

openalex publication_date 2010/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a theorem on separation of boundary null points for generators of continuous semigroups of holomorphic self-mappings of the unit disk in the complex plane. Our construction demonstrates the existence and importance of a particular role of the binary operation ∘ given by 1 / f ∘ g = 1/f + 1/g on generators.

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