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.