Minimal Models for N∞κ-functions

Aad Dijksma; Annemarie Luger; Yuri Shondin

Minimal Models for N∞κ-functions

Aad Dijksma, Annemarie Luger, Yuri Shondin

Systems, Control and Applied Analysis

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Abstract

We present explicit realizations in terms of self-adjoint operators and linear relations for a non-zero scalar generalized Nevanlinna function N(z) and the function ^N(z) = −1/N(z) under the assumption that ^N(z) has exactly one generalized pole which is not of positive type namely at z = ∞. The key tool we use to obtain these models is reproducing kernel Pontryagin spaces.

Original language	English
Title of host publication	EPRINTS-BOOK-TITLE
Publisher	University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science
Number of pages	38
Publication status	Published - 2005

Keywords

block operator matrix
linear relation
self-adjoint operator
symmetric operator
Pontryagin spaces
reproducing kernel spaces
model
realization
generalized pole
generalized Nevanlinna function

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abstract = "We present explicit realizations in terms of self-adjoint operators and linear relations for a non-zero scalar generalized Nevanlinna function N(z) and the function ^N(z) = −1/N(z) under the assumption that ^N(z) has exactly one generalized pole which is not of positive type namely at z = ∞. The key tool we use to obtain these models is reproducing kernel Pontryagin spaces.",

keywords = "block operator matrix, linear relation, self-adjoint operator, symmetric operator, Pontryagin spaces, reproducing kernel spaces, model, realization, generalized pole, generalized Nevanlinna function",

author = "Aad Dijksma and Annemarie Luger and Yuri Shondin",

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T1 - Minimal Models for N∞κ-functions

AU - Dijksma, Aad

AU - Luger, Annemarie

AU - Shondin, Yuri

N1 - Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen, Research Institute for Mathematics and Computing Science (IWI)

PY - 2005

Y1 - 2005

N2 - We present explicit realizations in terms of self-adjoint operators and linear relations for a non-zero scalar generalized Nevanlinna function N(z) and the function ^N(z) = −1/N(z) under the assumption that ^N(z) has exactly one generalized pole which is not of positive type namely at z = ∞. The key tool we use to obtain these models is reproducing kernel Pontryagin spaces.

AB - We present explicit realizations in terms of self-adjoint operators and linear relations for a non-zero scalar generalized Nevanlinna function N(z) and the function ^N(z) = −1/N(z) under the assumption that ^N(z) has exactly one generalized pole which is not of positive type namely at z = ∞. The key tool we use to obtain these models is reproducing kernel Pontryagin spaces.

KW - block operator matrix

KW - linear relation

KW - self-adjoint operator

KW - symmetric operator

KW - Pontryagin spaces

KW - reproducing kernel spaces

KW - model

KW - realization

KW - generalized pole

KW - generalized Nevanlinna function

M3 - Chapter

BT - EPRINTS-BOOK-TITLE

PB - University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science

ER -

Minimal Models for N∞κ-functions

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