Approximation of N∞ κ -functions I : Models and regularization
(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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https://lup.lub.lu.se/record/41815df7-f0ba-455b-bd01-cbffe49bde02
- author
- Dijksma, Aad ; Luger, Annemarie LU and Shondin, Yuri
- organization
- publishing date
- 2008
- 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
- 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
- 2025-01-12 12:09:34
@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 = {{02550156}}, 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}}, }