Proper holomorphic mappings vs. peak points and Silov boundary

2011/10/10 by Włodzimierz Zwonek, W. Zwonek, Łukasz Kosiński +3
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV

paper · pdf · doi:10.48550/arxiv.1110.2132

To appear in Ann. Pol. Math

openalex publication_date 2011/10/10 · arxiv created 2012/05/15 · arxiv updated 2012/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Peak functions in \mathbb C-convex domains
• Nonexistence of Continuous Peaking Functions
• Peak functions and boundary behaviour of holomorphically invariant distances on strictly pseudoconvex domains
• On holomorphic mappings of strictly pseudoconvex domains
• Condition R and proper holomorphic maps between equidimensional product domains