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

Daniel Alpay; Ariel Pinhas; Victor Vinnikov

doi:10.1016/j.aim.2020.107315

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

Daniel Alpay, Ariel Pinhas, Victor Vinnikov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English
Article number	107315
Journal	Advances in Mathematics
Volume	373
DOIs	https://doi.org/10.1016/j.aim.2020.107315
State	Published - 28 Oct 2020

Keywords

Beurling-Lax theorem
Compact Riemann surface
Joint transfer function
Operator vessels
de Branges Rovnyak spaces

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2020.107315

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title = "de Branges spaces on compact Riemann surfaces and a Beurling-Lax type theorem",

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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N2 - 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.

AB - 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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KW - Compact Riemann surface

KW - Joint transfer function

KW - Operator vessels

KW - de Branges Rovnyak spaces

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

Abstract

Keywords

ASJC Scopus subject areas

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