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# Generalized zeros and poles of $\mathcal N_\kappa$-functions: on the underlying spectral structure

### Abstract

Let $q$ be a scalar generalized Nevanlinna function, $q\in\mathcal N_\kappa$. Its gene alized zeros and poles (including their orders) are defined in terms of the function's operator representation. In this paper analytic properties associated with the underlying root subspaces and their geometric structures are investigated in terms of the local behaviour of the function. The main results and various characterizations are expressed by means of (local) moments, asymptotic expansions, and via the basic factorization of $q$. Also an inverse problem for recovering the geometric structure of the root subspace from an appropriate asymptotic expansion is solved.

### Article Information

 Title Generalized zeros and poles of $\mathcal N_\kappa$-functions: on the underlying spectral structure Source Methods Funct. Anal. Topology, Vol. 12 (2006), no. 2, 131-150 MathSciNet MR2238035 Copyright The Author(s) 2006 (CC BY-SA)

### Authors Information

Seppo Hassi
Department of Mathematics and Statistics, University of Vaasa, P.O. Box 700, 65101 Vaasa, Finland

Annemarie Luger
Institute of Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstrasse 8--10, A-1040 Wien, Austria

### Citation Example

Seppo Hassi and Annemarie Luger, Generalized zeros and poles of $\mathcal N_\kappa$-functions: on the underlying spectral structure, Methods Funct. Anal. Topology 12 (2006), no. 2, 131-150.

### BibTex

@article {MFAT360,
AUTHOR = {Hassi, Seppo and Luger, Annemarie},
TITLE = {Generalized zeros and poles of $\mathcal N_\kappa$-functions: on the underlying spectral structure},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {12},
YEAR = {2006},
NUMBER = {2},
PAGES = {131-150},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=360},
}