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 language | English |
---|---|
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