M. Langer and H. Woracek,
Distributional representations of 𝒩κ(∞)-functions,
Math. Nachr. 288 (2015), 1127–1149

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.

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