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https://scigraph.springernature.com/explorer/license/
The basic interpolation problem for Schur functions is: Find all Schur functions s(z)for which s (0) has a given value. In this paper we consider the same basic interpolation problem but now for the class of generalized Schur functions with finitely many negative squares which are holomorphic at z = 0. In Section3 its solutions are given by three fractional linear transformations in which the main parameter runs through a subset of the class of generalized Schur functions. A generalized Schur function can be written as the characteristic function of a minimal coisometric colligation with a Pontryagin state space. In the second part of this paper we describe the colligation of a solution s(z) of the basic interpolation problem for generalized Schur functions in terms of the colligation of the corresponding parameter function and the interpolation data. First we consider the canonical coisometric realization of s(z) in which the state space is the reproducing kernel Pontryagin space with kernel ;see for example [6]. In the final section we follow a direct approach more in line with [2, 3].
https://link.springer.com/10.1007%2F978-3-0348-8077-0_2
2019-04-16T08:57
A Basic Interpolation Problem for Generalized Schur Functions and Coisometric Realizations
en
chapter
2003
false
2003-01-01
978-3-0348-8077-0
Reproducing Kernel Spaces and Applications
978-3-0348-9430-2
doi
10.1007/978-3-0348-8077-0_2
Pure Mathematics
Mathematical Sciences
Ben-Gurion University of the Negev
Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, 84105, Beer-Sheva, Israel
Springer Nature - SN SciGraph project
Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands
University of Groningen
Wanjala
G.
T. Ya.
Azizov
TU Wien
Institute of Analysis and Technical Mathematics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040, Vienna, Austria
Daniel
Alpay
Voronezh State University
Department of Mathematics, Voronezh State University, 394693, Voronezh, Russia
Alpay
D.
A.
Dijksma
H.
Langer
Basel
BirkhĂ¤user Basel
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