A characterization of equality between de Branges--Rovnyak and Dirichlet spaces
We characterize when a de Branges--Rovnyak space coincides with a harmonically weighted Dirichlet space. We obtain a necessary and sufficient condition for this identification, which settles a long-standing open problem. We illustrate the result with several examples, that include measures supported on uncountable sets.
Authors
- Shuaibing Luo (ORCID: https://orcid.org/0000-0001-7288-750X)
- Carlo Bellavita (ORCID: https://orcid.org/0000-0003-3136-0271)
- Eugenio Dellepiane (ORCID: https://orcid.org/0009-0005-3432-2053)
Publication Details
- Journal
- arXiv (Cornell University)
- Published
- 2026-10-27
- DOI
- https://doi.org/10.48550/arxiv.2610.36943
- Primary Topic
- Holomorphic and Operator Theory
- Type
- preprint