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

 

Realization of nonstrict matrix Nevanlinna functions as Weyl functions of symmetric operators in Pontryagin spaces


Author: Jussi Behrndt
Journal: Proc. Amer. Math. Soc. 137 (2009), 2685-2696
MSC (2000): Primary 47B50, 30E99; Secondary 47B25, 47A56, 47A48
Published electronically: February 3, 2009
MathSciNet review: 2497481
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Abstract: Matrix-valued Nevanlinna functions with possibly noninvertible imaginary part are realized as $ Q$-functions or Weyl functions of symmetric operators in Pontryagin spaces. The functions are decomposed into a constant part, which gives rise to a realization in a finite dimensional Pontryagin space $ \mathcal{K}$, and a strict or uniformly strict part, which gives rise to a realization in a Hilbert space $ \mathcal{H}$. A coupling procedure then leads to a symmetric operator in the product space $ \mathcal{H}\times\mathcal{K}$ and to the realization of the given Nevanlinna function.


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Additional Information

Jussi Behrndt
Affiliation: Department of Mathematics MA 6–4, Technische Universität Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany
Email: behrndt@math.tu-berlin.de

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09812-8
PII: S 0002-9939(09)09812-8
Received by editor(s): January 30, 2008
Received by editor(s) in revised form: October 20, 2008
Published electronically: February 3, 2009
Communicated by: Marius Junge
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.