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arXiv · 2610.36943

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

Carlo Bellavita·Eugenio Dellepiane·Shuaibing Luo
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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.

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Carlo Bellavita, Eugenio Dellepiane, Shuaibing Luo. 2026-10-27. A characterization of equality between de Branges--Rovnyak and Dirichlet spaces. https://arxiv.org/abs/2610.36943

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