Distributional representations of N-kappa((infinity))-functions

作者：Langer Matthias^*; Woracek Harald

来源：Mathematische Nachrichten, 2015, 288(10): 1127-1149.

DOI：10.1002/mana.201300280

• Generalized Nevanlinna function
• distributional representation
• generalized pole of non-positive type
• operator model

The subclasses N-kappa((infinity)) of the classes N. 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 N-kappa((infinity)) -functions as Cauchy-type integrals in a distributional sense and characterize the class of distributions occurring in such representations. Wemake explicit howthe Pontryagin space model of an N-kappa((infinity)) - function is related to the multiplication operator in the L-2-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.

• 出版日期2015-7