PreprintCC BY-NC-ND 4.0arXiv
A characterization of equality between de Branges--Rovnyak and Dirichlet spaces
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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BibTeX
@misc{bellavita2026characterization,
title = {{A characterization of equality between de Branges--Rovnyak and Dirichlet spaces}},
author = {Carlo Bellavita and Eugenio Dellepiane and Shuaibing Luo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36943},
eprint = {2610.36943},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36943},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A characterization of equality between de Branges--Rovnyak and Dirichlet spaces
AU - Carlo Bellavita
AU - Eugenio Dellepiane
AU - Shuaibing Luo
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36943
UR - https://arxiv.org/abs/2610.36943
AB - 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.
ER -