Realizations of Slice Hyperholomorphic Generalized Contractive and Positive Functions

Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz, Irene Sabadini

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


We introduce generalized Schur functions and generalized positive functions in the setting of slice hyperholomorphic functions and study their realizations in terms of associated reproducing kernel Pontryagin spaces. To this end, we also prove some results in quaternionic functional analysis like an invariant subspace theorem for contractions in a Pontryagin space. We also consider slice hyperholomorphic functions on the half space $${\mathbb{H}_{+}}$$H+ of quaternions with positive real parts and we study the Hardy space H2$${(\mathbb{H}_{+})}$$(H+) and Blaschke products in this framework.

Original languageEnglish
Pages (from-to)91-144
Number of pages54
JournalMilan Journal of Mathematics
Issue number1
StatePublished - 18 Jun 2015


  • Primary 47B32
  • Secondary 30G35

ASJC Scopus subject areas

  • Mathematics (all)


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