Opuscula Math. 36, no. 6 (2016), 749-768
http://dx.doi.org/10.7494/OpMath.2016.36.6.749

 
Opuscula Mathematica

Minimal realizations of generalized Nevanlinna functions

Seppo Hassi
Hendrik Luit Wietsma

Abstract. Minimal realizations of generalized Nevanlinna functions that carry the information on their generalized poles of nonpositive type in an explicit form are established. These realizations are based on a modification of the basic canonical factorization of generalized Nevanlinna functions whereby the non-minimality problems in realizations that are based directly on the canonical factorization are circumvented.

Keywords: generalized Nevanlinna functions, selfadjoint (multi-valued) operators, (minimal) realizations.

Mathematics Subject Classification: 30E20, 46C20, 47B50.

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  • Seppo Hassi
  • University of Vaasa, Department of Mathematics and Statistics, P.O. Box 700, 65101 Vaasa, Finland
  • Hendrik Luit Wietsma
  • University of Vaasa, Department of Mathematics and Statistics, P.O. Box 700, 65101 Vaasa, Finland
  • Communicated by S.N. Naboko.
  • Received: 2016-05-04.
  • Revised: 2016-09-20.
  • Accepted: 2016-09-20.
  • Published online: 2016-10-29.
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Cite this article as:
Seppo Hassi, Hendrik Luit Wietsma, Minimal realizations of generalized Nevanlinna functions, Opuscula Math. 36, no. 6 (2016), 749-768, http://dx.doi.org/10.7494/OpMath.2016.36.6.749

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