Realization of nonstrict matrix Nevanlinna functions as Weyl functions of symmetric operators in Pontryagin spaces
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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.References
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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
- MR Author ID: 760074
- Email: behrndt@math.tu-berlin.de
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2685-2696
- MSC (2000): Primary 47B50, 30E99; Secondary 47B25, 47A56, 47A48
- DOI: https://doi.org/10.1090/S0002-9939-09-09812-8
- MathSciNet review: 2497481