de Branges-Rovnyak spaces which are complete Nevanlinna-Pick spaces
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| Format: | Preprint |
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2024
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| _version_ | 1866912523923488768 |
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| author | Ahmed, Hamidul Das, B. Krishna Panja, Samir |
| author_facet | Ahmed, Hamidul Das, B. Krishna Panja, Samir |
| contents | We consider de Branges-Rovnyak spaces of a considerably large class of reproducing kernel Hilbert spaces and find a characterization for them to be complete Nevanlinna-Pick spaces. This extends as well as recovers earlier characterizations obtained for the Hardy space over the unit disc (\cite{Chu}) as well as for the Drury-Arveson space over the unit ball (\cite{Jesse}). Our characterization takes a complete form for the particular cases of the Hardy space over the polydisc and the Bergman space over the disc. We show that a non-trivial de Branges-Rovnyak space, associated to a contractive multiplier, of the Hardy space over the bidisc or the Bergman space over the unit disc is a complete Nevanlinna-Pick space if and only if it is isometrically isomorphic to the Hardy space over the unit disc. On the contrary, it is shown that non-trivial de Branges-Rovnyak spaces of the Hardy space over the $n$-disc with $n\ge 3$ are never complete Nevanlinna-Pick spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_19377 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | de Branges-Rovnyak spaces which are complete Nevanlinna-Pick spaces Ahmed, Hamidul Das, B. Krishna Panja, Samir Functional Analysis We consider de Branges-Rovnyak spaces of a considerably large class of reproducing kernel Hilbert spaces and find a characterization for them to be complete Nevanlinna-Pick spaces. This extends as well as recovers earlier characterizations obtained for the Hardy space over the unit disc (\cite{Chu}) as well as for the Drury-Arveson space over the unit ball (\cite{Jesse}). Our characterization takes a complete form for the particular cases of the Hardy space over the polydisc and the Bergman space over the disc. We show that a non-trivial de Branges-Rovnyak space, associated to a contractive multiplier, of the Hardy space over the bidisc or the Bergman space over the unit disc is a complete Nevanlinna-Pick space if and only if it is isometrically isomorphic to the Hardy space over the unit disc. On the contrary, it is shown that non-trivial de Branges-Rovnyak spaces of the Hardy space over the $n$-disc with $n\ge 3$ are never complete Nevanlinna-Pick spaces. |
| title | de Branges-Rovnyak spaces which are complete Nevanlinna-Pick spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2403.19377 |