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math.FA2018★ 1 cited
Commuting operators over Pontryagin spaces with applications to system theory
Daniel Alpay, Ariel Pinhas, Victor Vinnikov
In this paper we extend vessel theory, or equivalently, the theory of overdetermined systems to the Pontryagin space setting. We focus on realization theorems of the various c…
math.CV2018
de Branges spaces on compact Riemann surfaces and a Beurling-Lax type theorem
Daniel Alpay, Ariel Pinhas, Victor Vinnikov
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 differe…