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arXiv · 1806.10704

Commuting operators over Pontryagin spaces with applications to system theory

Daniel Alpay·Ariel Pinhas·Victor Vinnikov
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Abstract

In this paper we extend vessel theory, or equivalently, the theory of overdetermined $2D$ systems to the Pontryagin space setting. We focus on realization theorems of the various characteristic functions associated to such vessels. In particular, we develop an indefinite version of de Branges-Rovnyak theory over real compact Riemann surfaces. To do so, we use the theory of contractions in Pontryagin spaces and the theory of analytic kernels with a finite number of negative squares. Finally, we utilize the indefinite de Branges-Rovnyak theory on compact Riemann surfaces in order to prove a Beurling type theorem on indefinite Hardy spaces on finite bordered Riemann surfaces.

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Daniel Alpay, Ariel Pinhas, Victor Vinnikov. 2018-06-27. Commuting operators over Pontryagin spaces with applications to system theory. https://arxiv.org/abs/1806.10704

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