Proper holomorphic mappings vs. peak points and Silov boundary

TL;DR

This paper investigates peak functions and peak points for specific complex domains, demonstrating their properties under proper holomorphic mappings and providing a description for certain Reinhardt domains.

Contribution

It introduces new results on peak functions for $ ext{C}$-convex domains and symmetrized polydiscs, and shows the invariance of peak points under proper holomorphic maps.

Findings

Existence of peak functions for $ ext{C}$-convex domains and symmetrized polydiscs.

Invariance of peak points under proper holomorphic mappings.

Characterization of peak points in bounded pseudoconvex Reinhardt domains.

Abstract

We present a result on existence of some kind of peak functions for $\C$-convex domains and for the symmetrized polydisc. Then we apply the latter result to show the equivariance of the set of peak points for $A(D)$ under proper holomorphic mappings. Additionally, we present a description of the set of peak points in the class of bounded pseudoconvex Reinhardt domains.