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arXiv · 2409.19299

De Branges-Rovnyak spaces generated by row Schur functions with mate

Hongxin Chen·Caixing Gu·Shuaibing Luo
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Abstract

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 $\dim (aH^2)^\perp < \infty$.

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Hongxin Chen, Caixing Gu, Shuaibing Luo. 2024-09-28. De Branges-Rovnyak spaces generated by row Schur functions with mate. https://arxiv.org/abs/2409.19299

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