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.87112 Abstract
The class N^{∞} _{κ} consists of all generalized Nevanlinna functions N with κ negative squares for which the root space at ∞ of the selfadjoint relation in the minimal model (short for selfadjoint operator realization) of N contains a κdimensional nonpositive 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:
http://lup.lub.lu.se/record/41815df7f0ba455bbd01cbffe49bde02
 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, Selfadjoint 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
 41815df7f0ba455bbd01cbffe49bde02
 date added to LUP
 20160926 14:15:43
 date last changed
 20170312 04:36:15
@inproceedings{41815df7f0ba455bbd01cbffe49bde02, 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 selfadjoint relation in the minimal model (short for selfadjoint operator realization) of N contains a κdimensional nonpositive 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,Selfadjoint operator,Symmetric operator}, language = {eng}, pages = {87112}, publisher = {Springer International Publishing}, title = {Approximation of N<sup>∞</sup> <sub>κ</sub> functions I : Models and regularization}, volume = {188}, year = {2008}, }