De Branges-Rovnyak spaces generated by row Schur functions with mate
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917789277618176 |
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| author | Chen, Hongxin Gu, Caixing Luo, Shuaibing |
| author_facet | Chen, Hongxin Gu, Caixing Luo, Shuaibing |
| contents | In this paper, we study the de Branges-Rovnyak spaces $\mathcal{H}(B)$ generated by row Schur functions $B$ with mate $a$. We prove that the polynomials are dense in $\mathcal{H}(B)$, and characterize the backward shift invariant subspaces of $\mathcal{H}(B)$. We then describe the cyclic vectors in $\mathcal{H}(B)$ when $B$ is of finite rank and $\dim (aH^2)^\perp < \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19299 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | De Branges-Rovnyak spaces generated by row Schur functions with mate Chen, Hongxin Gu, Caixing Luo, Shuaibing Functional Analysis Complex Variables In this paper, we study the de Branges-Rovnyak spaces $\mathcal{H}(B)$ generated by row Schur functions $B$ with mate $a$. We prove that the polynomials are dense in $\mathcal{H}(B)$, and characterize the backward shift invariant subspaces of $\mathcal{H}(B)$. We then describe the cyclic vectors in $\mathcal{H}(B)$ when $B$ is of finite rank and $\dim (aH^2)^\perp < \infty$. |
| title | De Branges-Rovnyak spaces generated by row Schur functions with mate |
| topic | Functional Analysis Complex Variables |
| url | https://arxiv.org/abs/2409.19299 |