Distributional representations of Nκ(∞) -functions

Langer, Matthias and Woracek, Harald (2015) Distributional representations of Nκ(∞) -functions. Mathematische Nachrichten, 288 (10). pp. 1127-1149. ISSN 0025-584X

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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.