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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A reproducing kernel space model for $\mathbf{N}_\kappa$-functions


Authors: Vladimir Derkach and Seppo Hassi
Journal: Proc. Amer. Math. Soc. 131 (2003), 3795-3806
MSC (2000): Primary 47B25, 47B50; Secondary 46C20, 46E22
Published electronically: March 25, 2003
MathSciNet review: 1999926
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Abstract: A new model for generalized Nevanlinna functions $Q\in\mathbf{N}_\kappa$ will be presented. It involves Bezoutians and companion operators associated with certain polynomials determined by the generalized zeros and poles of $Q$. The model is obtained by coupling two operator models and expressed by means of abstract boundary mappings and the corresponding Weyl functions.


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Additional Information

Vladimir Derkach
Affiliation: Department of Mathematics, Donetsk National University, Universitetskaya str. 24, 83055 Donetsk, Ukraine
Address at time of publication: Department of Mathematics, Western Washington University, Bellingham, Washington 98225
Email: derkacv@cc.wwu.edu

Seppo Hassi
Affiliation: Department of Mathematics and Statistics, University of Vaasa, PL 700, 65101 Vaasa, Finland
Email: sha@uwasa.fi

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06946-6
PII: S 0002-9939(03)06946-6
Keywords: Generalized Nevanlinna function, symmetric operator, selfadjoint extension, Weyl function, boundary triplet, reproducing kernel Pontryagin space
Received by editor(s): December 7, 2001
Received by editor(s) in revised form: July 10, 2002
Published electronically: March 25, 2003
Additional Notes: The support of the Academy of Finland (projects 40362 and 52528) is gratefully acknowledged
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society