Distributional representations of Nκ(∞) -functions

Matthias Langer, Harald Woracek

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Abstract

The subclasses Nκ(∞) of the classes Nκ 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 Nκ(∞)-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 Nκ(∞)-function is related to the multiplication operator in the L2-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 languageEnglish
Pages (from-to)1127-1149
Number of pages23
JournalMathematische Nachrichten
Volume288
Issue number10
Early online date12 Feb 2015
DOIs
Publication statusPublished - Jul 2015

Keywords

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

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