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Minimal realizations of generalized Nevanlinna functions

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Strony
749--768
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
  • University of Vaasa Department of Mathematics and Statistics P.O. Box 700, 65101 Vaasa, Finland
  • University of Vaasa Department of Mathematics and Statistics P.O. Box 700, 65101 Vaasa, Finland
Bibliografia
  • [1] J. Behrndt, V. Derkach, S. Hassi, H.S.V. de Snoo, A realization theorem for generalized Nevanlinna families, Operators and Matrices 5 (2011) 4, 679-706.
  • [2] V.A. Derkach, S. Hassi, A reproducing kernel space model for Mr,-functions, Proc. Amer. Math. Soc. 131 (2003), 3795-3806.
  • [3] V.A. Derkach, S. Hassi, H.S.V. de Snoo, Operator models associated with Kac subclasses of generalized Nevanlinna functions, Methods of Funct. Anal, and Top. 5 (1999), 65-87.
  • [4] V.A. Derkach, S. Hassi, H.S.V. de Snoo, A factorization model for the generalized Friedrichs extension in a Pontryagin space, Oper. Theory Adv. Appl. 162 (2005), 117-133.
  • [5] V.A. Derkach, S. Hassi, H.S.V. de Snoo, Asymptotic expansions of generalized Nevanlinna functions and their spectral properties, Oper. Theory Adv. Appl. 175 (2007), 51-88.
  • [6] A. Dijksma, H. Langer, A. Luger, Yu. Shondin, A factorization result for generalized Nevanlinna functions of the class NK, Integral Equations Operator Theory 36 (2000), 121-125.
  • [7] A. Dijksma, H. Langer, A. Luger, Yu. Shondin, Minimal realizations of scalar generalized Nevanlinna functions related to their basic factorization, Oper. Theory Adv. Appl. 154 (2004), 69-90.
  • [8] A. Dijksma, H. Langer, H.S.V. de Snoo, Eigenvalues and pole functions of Hamiltonian systems with eigenvalue depending boundary conditions, Math. Nachr. 161 (1993), 107-154.
  • [9] A. Dijksma, H.S.V. de Snoo, Symmetric and selfadjoint relations in Krem spaces I, Oper. Theory Adv. Appl. 24 (1987), 145-166.
  • [10] S. Hassi, H. Langer, H.S.V. de Snoo, Selfadjoint extensions for a class of symmetric operators with defect numbers (1,1), 15th OT Conference Proceedings, 1995, 115-145.
  • [11] S. Hassi, H.S.V. de Snoo, H. Woracek, Some interpolation problems of Nevanlinna-Pick type, Oper. Theory Adv. Appl. 106 (1998), 201-216.
  • [12] I.S. Kac, M.G. Krem, R-functions - analytic functions mapping the upper halfplane into itself, Amer. Math. Soc. Transl. 103 (1974), 1-18.
  • [13] P. Koosis, Introduction to Hv Spaces, 2nd ed., Cambridge University Press, Cambridge, 1998.
  • [14] M.G. Krem, H. Langer, Uber die Q-Funktion eines n-herm/iteschen Operators im Raurne UK, Acta Sci. Math. (Szeged) 34 (1973), 191-230.
  • [15] M.G. Krein, H. Langer, Uber einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im, Raum I1K zusammenhangen, I. Einige Funktionenklassen und ihre Darstellungen, Math. Nachr. 77 (1977), 187-236.
  • [16] M.G. Krem, H. Langer, Some propositions on analytic matrix functions related to the theory of operators in the space I1K, Acta Sci. Math. 43 (1981), 181-205.
  • [17] H. Langer, A characterization of generalized zeros of negative type of functions of the class 9tK, Oper. Theory: Adv. Appl. 17 (1986), 201-212.
  • [18] A. Luger, A factorization of regular generalized Nevanlinna functions, Integral Equations Operator Theory 43 (2002), 326-345.
  • [19] H.L. Wietsma, Factorization of generalized Nevanlinna functions and the invariant subspace property, submitted.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9e7d03ab-7417-4c27-ac04-5c8c93429453
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