Approximation of N^{∞} _{κ} functions I : Models and regularization
(2008) 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, 2006 In Spectral Theory in Inner Product Spaces and Applications  6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, 2006 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
 Spectral Theory in Inner Product Spaces and Applications  6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, 2006
 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
 22964878
 02550156
 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 = {Spectral Theory in Inner Product Spaces and Applications  6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, 2006}, isbn = {9783764389109}, issn = {22964878}, 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}, }