## Abstract

Loewner's theorem on boundary interpolation of N_{κ} 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 N_{κ} 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 N_{κ} functions in terms of selfadjoint relations in Pontryagin spaces and the extension theory of symmetric relations in Pontryagin spaces.

Original language | English |
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Pages (from-to) | 2057-2066 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 130 |

Issue number | 7 |

DOIs | |

State | Published - 1 Jan 2002 |

## ASJC Scopus subject areas

- Mathematics (all)
- Applied Mathematics

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