Herglotz functions: The Fueter variables case

Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Research output: Contribution to journalArticlepeer-review


In this paper we provide realizations of Herglotz functions in the quaternionic case where hyperholomorphic functions are meant in the sense of Fueter. We consider the counterparts of the Arveson space and of the Herglotz–Agler functions by introducing suitable positive kernels. Crucial tools are the so-called Fueter variables and the CK-product. Our realization results also show that positivity implies analyticity.

Original languageEnglish
Pages (from-to)75-97
Number of pages23
JournalLinear Algebra and Its Applications
StatePublished - 15 Feb 2019
Externally publishedYes


  • Arveson space
  • Fueter variables
  • Herglotz functions

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'Herglotz functions: The Fueter variables case'. Together they form a unique fingerprint.

Cite this