A characterization of equality between de Branges--Rovnyak and Dirichlet spaces
Carlo Bellavita, Eugenio Dellepiane, Shuaibing Luo
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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