Commuting operators over Pontryagin spaces with applications to system theory

Daniel Alpay, Ariel Pinhas, Victor Vinnikov

Research output: Contribution to journalArticlepeer-review


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
Article number109864
JournalJournal of Functional Analysis
Issue number10
StatePublished - 15 May 2023


  • Compact Riemann surface
  • Joint transfer function
  • Pontryagin spaces
  • de Branges-Rovnyak spaces

ASJC Scopus subject areas

  • Analysis


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