On the Loewner problem in the class Nκ

Dany Alpay, A. Dijksma, H. Langer

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Loewner's theorem on boundary interpolation of Nκ functions is proved under rather general conditions. In particular, the hypothesis of Alpay and Rovnyak (1999) that the function f, which is to be extended to an Nκ function, is defined and continuously differentiable on a nonempty open subset of the real line, is replaced by the hypothesis that the set on which f is defined contains an accumulation point at which f satisfies some kind of differentiability condition. The proof of the theorem in this note uses the representation of Nκ functions in terms of selfadjoint relations in Pontryagin spaces and the extension theory of symmetric relations in Pontryagin spaces.

Original languageEnglish
Pages (from-to)2057-2066
Number of pages10
JournalProceedings of the American Mathematical Society
Issue number7
StatePublished - 1 Jan 2002

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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