Positive and Generalized Positive Real Lemma for Slice Hyperholomorphic Functions

Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz, Irene Sabadini

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic functions. We consider the case of functions with positive real part in the half space of quaternions with positive real part, as well as the case of (generalized) Schur functions in the open unit ball.

Original languageEnglish
Article number4
JournalIntegral Equations and Operator Theory
Issue number1
StatePublished - 1 Feb 2019


  • Half space
  • Kalman–Yakubovich–Popov lemma
  • Negative squares
  • Positive real functions
  • Slice hyperholomorphic functions
  • Unit ball

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


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