2025/12/19 by Michael Hartz, Hartz, Michael, Stefan Richter +1
Mathematics · #46E22 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Primary 30J05 #Secondary 30H25
paper · doi:10.48550/arxiv.2512.17723
openalex publication_date 2025/12/19 · openalex created_date 2025/12/23 · openalex updated_date 2026/07/28
Every function in the Dirichlet space on the unit disc has an inner/outer factorization. We study which inner functions occur in this way. For Blaschke products, this is the well known question of which subsets of the disc are zero sets for the Dirichlet space. We also consider singular inner factors, and in particular prove an analogue of the Shapiro-Shields theorem in this setting. Our results on singular inner factors also yield new sufficient conditions for zero sets.