de Branges spaces on compact Riemann surfaces and a Beurling-Lax type theorem

Daniel Alpay; Ariel Pinhas; Victor Vinnikov

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arXiv · 1806.08670

de Branges spaces on compact Riemann surfaces and a Beurling-Lax type theorem

Daniel Alpay·Ariel Pinhas·Victor Vinnikov

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Abstract

Using the notion of commutative operator vessels, this work investigates de Branges-Rovnyak spaces whose elements are sections of a line bundle of multiplicative half-order differentials on a compact real Riemann surface. As a special case, we obtain a Beurling-Lax type theorem in the setting of the corresponding Hardy space on a finite bordered Riemann surface.

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Daniel Alpay, Ariel Pinhas, Victor Vinnikov. 2018-06-22. de Branges spaces on compact Riemann surfaces and a Beurling-Lax type theorem. https://arxiv.org/abs/1806.08670

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