Reproducing kernel quaternionic pontryagin spaces

Daniel Alpay, Michael Shapiro

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


This paper studies various aspects of reproducing kernel spaces with a possibly indefinite metric when the field of scalar is replaced by the skew-field of quaternions. We first discuss in some details the positive case. A key fact which allows to consider the non-positive case is that Hermitian matrices with quaternionic entries have only real eigenvalues. This permits to extend the notion of functions with a finite number of negative squares to the present setting and we prove in particular that there is a one-to-one correspondence between such functions and reproducing kernel Pontryagin quaternionic spaces.

Original languageEnglish
Pages (from-to)431-476
Number of pages46
JournalIntegral Equations and Operator Theory
Issue number4
StatePublished - 1 Dec 2004


  • Hyperholomorphic functions
  • Pontryagin spaces
  • Reproducing kernel spaces

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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