Separation of Boundary Singularities for Holomorphic Generators

TL;DR

This paper establishes a theorem on boundary null points for holomorphic semigroup generators in the unit disk, highlighting the significance of a specific binary operation on these generators.

Contribution

It introduces a novel theorem on boundary singularities and emphasizes the role of a binary operation in the structure of holomorphic generators.

Findings

Existence of boundary null points for generators

Importance of the binary operation on generators

Theoretical insights into boundary behavior of holomorphic semigroups

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 $\circ$ given by $1 / f \circ g = 1/f + 1/g$ on generators.