2021/08/02 by Javad Mashreghi, Thomas Ransford, Mashreghi, Javad +1
Mathematics · #46E22 #46F05 #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #math.FA #msc:46E22 #msc:46F05
paper · pdf · doi:10.48550/arxiv.2108.01185
openalex publication_date 2021/08/02 · arxiv created 2021/09/27 · arxiv updated 2021/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that if u is a compactly supported distribution on the complex plane such that, for every pair of entire functions f,g, ⟨ u,fg⟩=⟨ u,f⟩⟨ u,g⟩, then u is supported at a single point. As an application, we complete the classification of all weighted Dirichlet spaces on the unit disk that are de Branges-Rovnyak spaces by showing that, for such spaces, the weight is necessarily a superharmonic function.