Commuting operators over Pontryagin spaces with applications to system theory

Daniel Alpay, Ariel Pinhas, Victor Vinnikov

Research output: Working paper/PreprintPreprint

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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.
Original languageEnglish
PublisherarXiv:1806.10704 [math.FA]
StatePublished - 27 Jun 2018

Keywords

  • math.FA
  • math.CV
  • 46C20, 46E22, 47A48, 47A56, 47B32, 47B50

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