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arXiv · 2608.01461

Automorphic de Branges - Rovnyak Spaces

Alexander Kheifets
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Abstract

A family of automorphic de Branges - Rovnyak spaces (depending on an arbitrary character $\alpha$) is associated to a $\beta$-automorphic analytic function $w$ bounded in modulus by $1$. Multiplication by the Green function defines unitary operators acting between those spaces. Function $w$ can be recovered from these operators as the characteristic function. It is shown that for Nevanlinna-Pick problem this family of unitary operators extends the family of isometric operators defined by the interpolation data.

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Alexander Kheifets. 2026-08-02. Automorphic de Branges - Rovnyak Spaces. https://arxiv.org/abs/2608.01461

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