Orthogonal polynomials in de Branges--Rovnyak spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915831592517632 |
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| author | Dellepiane, Eugenio Seco, Daniel |
| author_facet | Dellepiane, Eugenio Seco, Daniel |
| contents | Given a function $b$, holomorphic on the disc and bounded by 1, one can construct an associated reproducing kernel Hilbert space called the de Branges--Rovnyak space $H(b)$. We explore representations of such spaces via descriptions of the corresponding families of orthogonal polynomials. We find relevant structures in the linear systems involved in a diversity of cases when $b$ is rational. We also establish a form of invariance under some composition operators on $H(b)$ spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03093 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Orthogonal polynomials in de Branges--Rovnyak spaces Dellepiane, Eugenio Seco, Daniel Complex Variables Functional Analysis Primary 30H45, Secondary 41A10, 42C05 Given a function $b$, holomorphic on the disc and bounded by 1, one can construct an associated reproducing kernel Hilbert space called the de Branges--Rovnyak space $H(b)$. We explore representations of such spaces via descriptions of the corresponding families of orthogonal polynomials. We find relevant structures in the linear systems involved in a diversity of cases when $b$ is rational. We also establish a form of invariance under some composition operators on $H(b)$ spaces. |
| title | Orthogonal polynomials in de Branges--Rovnyak spaces |
| topic | Complex Variables Functional Analysis Primary 30H45, Secondary 41A10, 42C05 |
| url | https://arxiv.org/abs/2603.03093 |