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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.

Please use this url to cite or link to this publication:
author
; and
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
host publication
Spectral Theory in Inner Product Spaces and Applications - 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, 2006
series title
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
conference location
Berlin, Germany
conference dates
2006-12-14 - 2006-12-17
external identifiers
  • scopus:84959139386
ISSN
22964878
02550156
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
2024-03-07 12:55:07
@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    = {{Spectral Theory in Inner Product Spaces and Applications - 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, 2006}},
  isbn         = {{9783764389109}},
  issn         = {{22964878}},
  keywords     = {{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}},
  series       = {{Operator Theory: Advances and Applications}},
  title        = {{Approximation of N<sup>∞</sup> <sub>κ</sub> -functions I : Models and regularization}},
  volume       = {{188}},
  year         = {{2008}},
}