de Branges spaces on compact Riemann surfaces and a Beurling-Lax type theorem (Q2196622)

The article under review deals with de Branges-Rovnyak spaces whose elements are sections of a line bundle of multiplicative half-order differentials on a compact real Riemann surface. Here a compact real Riemann surface is a compact Riemann surface equipped with an anti-holomorphic involution. Next, as an application, the authors obtain a Beurling-Lax type theorem in the setting of the corresponding Hardy space on a finite bordered Riemann surface. The approach is based on the theory of commutative operators vessels and operator model theory for pairs of commuting nonselfadjoint operators.