Contributions to Books:
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.
English abstract:
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.
Keywords:
Generalized Nevanlinna function, distributional representa tion, generalized pole of non-positive type, operator model
Electronic version of the publication:
http://www.asc.tuwien.ac.at/preprint/2013/asc17x2013.pdf
Created from the Publication Database of the Vienna University of Technology.