Work

A characterization of equality between de Branges--Rovnyak and Dirichlet spaces

Year: 2026

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.36943

Authors: Bellavita, Carlo, Dellepiane, Eugenio, Luo, Shuaibing

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

OpenAlex ID: W7224092363

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