Analytic solutions of convolution equations on convex sets with a mixed structure. II

TL;DR

This paper establishes conditions for the existence of continuous linear right inverses for convolution operators on spaces of analytic function germs over convex sets with mixed structures, based on boundary behavior of associated convex univalent functions.

Contribution

It provides new criteria for right invertibility of convolution operators on complex convex sets with a mixed structure, linking it to boundary properties of convex univalent functions.

Findings

Conditions for the existence of continuous linear right inverses are derived.

The criteria are expressed in terms of boundary behavior of convex univalent functions.

Applicable to convex sets with a countable neighborhood basis of convex domains.

Abstract

We prove conditions for the existence of a continuous linear right inverse for a surjective convolution operator in spaces of germs of analytic functions on convex subsets of the complex plane. Considered convex sets have a countable neighborhood basis of convex domains. Mentioned conditions are obtained in terms of the boundary behavior of convex univalent functions which are defined by these sets.