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 (https://doi.org/10.1002/mana.201300280)
Preview |
PDF.
Filename: Langer_Woracek_MN_2015_Distributional_representations_of_N_functions.pdf
Accepted Author Manuscript Download (474kB)| Preview |
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.
ORCID iDs
Langer, Matthias ORCID: https://orcid.org/0000-0001-8813-7914 and Woracek, Harald;-
-
Item type: Article ID code: 50123 Dates: DateEventJuly 2015Published12 February 2015Published Online24 October 2014AcceptedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 04 Nov 2014 10:45 Last modified: 01 Sep 2024 01:09 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/50123