Approximation of Nκ∞-functions I: Models and Regularization View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2008

AUTHORS

Aad Dijksma , Annemarie Luger , Yuri Shondin

ABSTRACT

The class Ngk∞ 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 ∈ Ngk∞: 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. More... »

PAGES

87-112

References to SciGraph publications

  • 1970-03. Diskrete Konvergenz linearer Operatoren. I in MATHEMATISCHE ANNALEN
  • 1966. Perturbation theory for linear operators in NONE
  • 2004. Minimal Realizations of Scalar Generalized Nevanlinna Functions Related to Their Basic Factorization in SPECTRAL METHODS FOR OPERATORS OF MATHEMATICAL PHYSICS
  • 2000. Self-adjoint Operators with Inner Singularities and Pontryagin Spaces in OPERATOR THEORY AND RELATED TOPICS
  • 1986. A Characterization of Generalized Zeros of Negative Type of Functions of the Class Nκ in ADVANCES IN INVARIANT SUBSPACES AND OTHER RESULTS OF OPERATOR THEORY
  • Book

    TITLE

    Spectral Theory in Inner Product Spaces and Applications

    ISBN

    978-3-7643-8910-9
    978-3-7643-8911-6

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-7643-8911-6_5

    DOI

    http://dx.doi.org/10.1007/978-3-7643-8911-6_5

    DIMENSIONS

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