On the equality of De Branges-Rovnyak and Dirichlet spaces
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| Format: | Preprint |
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2025
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| _version_ | 1866910966389669888 |
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| author | Dellepiane, Eugenio Peloso, Marco M. Tabacco, Anita |
| author_facet | Dellepiane, Eugenio Peloso, Marco M. Tabacco, Anita |
| contents | This work is devoted to the comparison of de Branges--Rovnyak $H(b)$ spaces harmonically weighted Dirichlet spaces $\mathcal{D}_μ$. We completely characterize which $H(b)$ spaces are also harmonically weighted Dirichlet spaces $\mathcal{D}_μ$, when $μ$ is a finite sum of atoms. This is a generalization of a previous result by Costara--Ransford \cite{costara2013}: we make no assumptions on the Pythagorean pair $(b,a)$, and we produce new examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_16572 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the equality of De Branges-Rovnyak and Dirichlet spaces Dellepiane, Eugenio Peloso, Marco M. Tabacco, Anita Functional Analysis Complex Variables 30H45, 30H10, 46E22, 30J99 This work is devoted to the comparison of de Branges--Rovnyak $H(b)$ spaces harmonically weighted Dirichlet spaces $\mathcal{D}_μ$. We completely characterize which $H(b)$ spaces are also harmonically weighted Dirichlet spaces $\mathcal{D}_μ$, when $μ$ is a finite sum of atoms. This is a generalization of a previous result by Costara--Ransford \cite{costara2013}: we make no assumptions on the Pythagorean pair $(b,a)$, and we produce new examples. |
| title | On the equality of De Branges-Rovnyak and Dirichlet spaces |
| topic | Functional Analysis Complex Variables 30H45, 30H10, 46E22, 30J99 |
| url | https://arxiv.org/abs/2505.16572 |