L_h²-functions in unbounded balanced domains

2016/09/05 by Peter Pflug, Włodzimierz Zwonek, Pflug, Peter +1 · 1 citation
Mathematics · #32A07 #32A36 #32D05 #32U25 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1609.01264

openalex publication_date 2016/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate problems related with the existence of square integrable holomorphic functions on (unbounded) balanced domains. In particular, we solve the problem of Wiegerinck for balanced domains in dimension two. We also give a description of L_h²-domains of holomorphy in the class of balanced domains and present a purely algebraic criterion for homogeneous polynomials to be square integrable in a pseudoconvex balanced domain in \mathbb C². This allows easily to decide which pseudoconvex balanced domain in \mathbb C² has a positive Bergman kernel and which admits the Bergman metric.

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