On the Loewner Problem in the Class Nκ
Daniel Alpay, Aad Dijksma, Heinz Langer · University of Groningen research database (University of Groningen / Centre for Information Technology) · 2002
Loewner's theorem on boundary interpolation of Nκ functions is proved under rather general conditions. In particular, the hypothesis 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.