2024/03/04 by Kenta Kojin, Kojin, Kenta
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Nonlinear Differential Equations Analysis
paper · pdf · doi:10.48550/arxiv.2403.02521
openalex publication_date 2024/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we will characterize those sets, over which every irreducible complete Nevanlinna--Pick space enjoys that its multiplier and supremum norms coincide. Moreover, we will prove that, if there exists an irreducible complete Nevanlinna--Pick space of holomorphic functions on a reduced complex space X whose multiplier algebra is isometrically equal to the algebra of bounded holomorphic functions (we will say that such a space is of Hardy type in this paper), then X must be biholomorphic to the unit disk minus a zero analytic capacity set. This means that the Hardy space is characterized as a unique irreducible complete Nevanlinna--Pick space of Hardy type.