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Spectral Theory in Inner Product Spaces and Applications pp 87–112Cite as

Approximation of N ∞κ -functions I: Models and Regularization

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 188))

Abstract

The class N ∞gk consists of all generalized Nevanlinna functions N with κ negative squares for which the root space at ∞ of the self-adjoint relation in the minimal model (short for self-adjoint operator realization) of N contains a κ-dimensional non-positive subspace. In this paper we discuss two specific models for the function N ∈ N ∞gk : one associated with the irreducible representation of N and one associated with a regularized version of this representation which need not be irreducible. The state space in each of these models is a reproducing kernel Pontryagin space whose reproducing kernel is a matrix function constructed from the data in the representation.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Groningen, P.O. Box 407, 9700, AK Groningen, The Netherlands

    Aad Dijksma

  2. Department of Mathematics, Lund Institute of Technology, Box 118, SE-221 00, Lund, Sweden

    Annemarie Luger

  3. Department of theoretical Physics, State Pedagogical University, Str. Ulyanova 1, Nizhny Novgorod, GSP 37, 603950, Russia

    Yuri Shondin

Authors
  1. Aad Dijksma
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  2. Annemarie Luger
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  3. Yuri Shondin
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, MA 6-4, 10623, Berlin, Germany

    Jussi Behrndt  & Karl-Heinz Förster  & 

  2. Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstraße 8, 1040, Wien, Austria

    Heinz Langer

  3. Institut für Mathematik, Technische Universität Ilmenau, Postfach 100565, 98684, Ilmenau, Germany

    Carsten Trunk

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Dijksma, A., Luger, A., Shondin, Y. (2008). Approximation of N ∞κ -functions I: Models and Regularization. In: Behrndt, J., Förster, KH., Langer, H., Trunk, C. (eds) Spectral Theory in Inner Product Spaces and Applications. Operator Theory: Advances and Applications, vol 188. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8911-6_5

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