M. Langer, H. Woracek:

"Distributional representations of ${\mathcal N}_{\kappa}^{(infty)}$-functions";

in: "ASC Report 17/2013", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2013, ISBN: 978-3-902627-06-3, 1 - 28.

The subclasses N(1) of the classes N of generalized Nevanlinna func-

tions 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 di erential expressions with singular coe cients. We study representations of N(1}-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 N(1)-function is related to the mul-

tiplication operator in the L2-space of the measure which describes the action of the representing distribution away from in nity. Moreover, we determine the distributional representations of a pair of functions associated with a symmetric generalized Nevanlinna function.

Generalized Nevanlinna function, distributional representa tion, generalized pole of non-positive type, operator model

http://www.asc.tuwien.ac.at/preprint/2013/asc17x2013.pdf

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