On the equality of De Branges-Rovnyak and Dirichlet spaces

2025/05/22 by Eugenio Dellepiane, Dellepiane, Eugenio, Marco M. Peloso +3
Mathematics · #30H10 #30H45 #30J99 #46E22 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2505.16572

openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work is devoted to the comparison of de Branges--Rovnyak H(b) spaces harmonically weighted Dirichlet spaces D_μ. We completely characterize which H(b) spaces are also harmonically weighted Dirichlet spaces D_μ, when μ is a finite sum of atoms. This is a generalization of a previous result by Costara--Ransford \citecostara2013: we make no assumptions on the Pythagorean pair (b,a), and we produce new examples.

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