Boundary Interpolation for Slice Hyperholomorphic Schur Functions

Khaled Abu-Ghanem, Daniel Alpay, Fabrizio Colombo, David P. Kimsey, Irene Sabadini

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

A boundary Nevanlinna–Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers (Formula presenred.), quaternions p1,…,pN all of modulus 1, so that the 2-spheres determined by each point do not intersect and pu ≠ 1 for u = 1,…, N, and quaternions s1,…, sN, we wish to find a slice hyperholomorphic Schur function s so that(Formula presenred.).(Formula presenred.).Our arguments rely on the theory of slice hyperholomorphic functions and reproducing kernel Hilbert spaces.

Original languageEnglish
Pages (from-to)223-248
Number of pages26
JournalIntegral Equations and Operator Theory
Volume82
Issue number2
DOIs
StatePublished - 1 Jun 2015

Keywords

  • 30E05
  • 30G35
  • 47B32

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