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Approximation of N κ -functions I : Models and regularization

Dijksma, Aad; Luger, Annemarie LU and Shondin, Yuri (2008) 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, 2006 In Operator Theory: Advances and Applications 188. p.87-112
Abstract

The class N κ 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 κ: 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
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Generalized nevanlinna function, Linear relation, Model, Pontryagin space, Realization, Reproducing kernel space, Self-adjoint operator, Symmetric operator
in
Operator Theory: Advances and Applications
volume
188
pages
26 pages
publisher
Springer International Publishing
conference name
6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, 2006
external identifiers
  • scopus:84959139386
ISSN
02550156
22964878
ISBN
9783764389109
language
English
LU publication?
yes
id
41815df7-f0ba-455b-bd01-cbffe49bde02
date added to LUP
2016-09-26 14:15:43
date last changed
2017-03-12 04:36:15
@inproceedings{41815df7-f0ba-455b-bd01-cbffe49bde02,
  abstract     = {<p>The class N<sup>∞</sup> <sub>κ</sub> 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<sup>∞</sup> <sub>κ</sub>: 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.</p>},
  author       = {Dijksma, Aad and Luger, Annemarie and Shondin, Yuri},
  booktitle    = {Operator Theory: Advances and Applications},
  isbn         = {9783764389109},
  issn         = {02550156},
  keyword      = {Generalized nevanlinna function,Linear relation,Model,Pontryagin space,Realization,Reproducing kernel space,Self-adjoint operator,Symmetric operator},
  language     = {eng},
  pages        = {87--112},
  publisher    = {Springer International Publishing},
  title        = {Approximation of N<sup>∞</sup> <sub>κ</sub> -functions I : Models and regularization},
  volume       = {188},
  year         = {2008},
}