### Abstract

The subclasses N

_{κ}^{(∞)}of the classes N_{κ}of generalized Nevanlinna functions appear in the context of Pontryagin space models, where they correspond to model relations having a particular spectral behaviour. Applications are found, for instance, in the investigation of differential expressions with singular coefficients. We study representations of N_{κ}^{(∞)}-functions as Cauchy-type integrals in a distributional sense and characterize the class of distributions occurring in such representations. We make explicit how the Pontryagin space model of an N_{κ}^{(∞)}-function is related to the multiplication operator in the L^{2}-space of the measure which describes the action of the representing distribution away from infinity. Moreover, we determine the distributional representations of a pair of functions associated with a symmetric generalized Nevanlinna function.Original language | English |
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Pages (from-to) | 1127-1149 |

Number of pages | 23 |

Journal | Mathematische Nachrichten |

Volume | 288 |

Issue number | 10 |

Early online date | 12 Feb 2015 |

DOIs | |

Publication status | Published - Jul 2015 |

### Keywords

- generalized Nevanlinna function
- distributional representation
- generalized pole of non-positive type
- operator model

## Cite this

Langer, M., & Woracek, H. (2015). Distributional representations of N

_{κ}^{(∞)}-functions.*Mathematische Nachrichten*,*288*(10), 1127-1149. https://doi.org/10.1002/mana.201300280