The Nevanlinna-Pick interpolation problem in multiply connected domains

V. L. Vinnikov, S. I. Fedorov

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We simplify and strengthen Abrahamse's result on the Nevanlinna-Pick interpolation problem in a finitely connected planar domain, according to which the problem has a solution if and only if the Pick matrices associated with character-automorphic Hardy spaces are positive semidefinite for all characters in ℝn-1/ℤn-1, where n is the connectivity of the domain. The main aim of the paper is to reduce the indicated procedure (verification of the positive semidefiniteness) for the entire real (n-1)-torus ℝn-1/ℤn-1 to a part of it, whose dimension is, possibly, less than n-1.

Original languageEnglish
Pages (from-to)2109-2126
Number of pages18
JournalJournal of Mathematical Sciences
Issue number4
StatePublished - 1 Jan 2001
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Applied Mathematics


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