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Functional models for Nevanlinna families

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Abstrakty
EN
The class of Nevanlinna families consists of R-symmetric holomorphic multivalued functions on C \ R with maximal dissipative (maximal accumulative) values on C+ (C-, respectively) and is a generalization of the class of operator-valued Nevanlinna functions. In this note Nevanlinna families are realized as Weyl families of boundary relations induced by multiplication operators with the independent variable in reproducing kernel Hilbert spaces.
Rocznik
Strony
233--245
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
autor
autor
autor
  • Technische Universität Berlin Institut für Mathematik, MA 6-4 Strasse des 17. Juni 136, 10623 Berlin, Deutschland, behrndt@math.tu-berlin.de
Bibliografia
  • [1] D. Alpay, A. Dijksma, J. Rovnyak, H.S.V. de Snoo, Schur functions, operator colligations, and Pontryagin spaces, Oper. Theory Adv. Appl. 96, Birkh¨auser Verlag, Basel-Boston, 1997.
  • [2] J. Behrndt, S. Hassi, H.S.V. de Snoo, Boundary relations, unitary colligations, and functional models, Complex Analysis Operator Theory, to appear.
  • [3] L. de Branges, Hilbert spaces of entire functions, Prentice Hall, Englewood Cliffs, N.J. [French translation: Espaces hilbertiens de fonctions entières, Masson et Cie, Paris, 1972].
  • [4] V.A. Derkach, Abstract interpolation problem in Nevanlinna classes, arXiv:0710.5234v1.
  • [5] V.A. Derkach, S. Hassi, M.M. Malamud, H.S.V. de Snoo, Boundary relations and their Weyl families, Trans. Amer. Math. Soc. 358 (2006), 5351–5400.
  • [6] V.A. Derkach, M.M. Malamud, Generalized resolvents and the boundary value problems for hermitian operators with gaps, J. Funct. Anal. 95 (1991), 1–95.
  • [7] V.A. Derkach, M.M. Malamud, The extension theory of hermitian operators and the moment problem, J. Math. Sciences 73 (1995), 141–242.
  • [8] V.I. Gorbachuk, M.L. Gorbachuk, Boundary value problems for operator differential equations, Kluwer Academic Publishers, Dordrecht, 1991.
  • [9] M.G. Kreǐn, H. Langer, Uber die Q-function eines π-hermiteschen Operators im Raume Πk, Acta. Sci. Math. (Szeged) 34 (1973), 191–230.
  • [10] H. Langer, B. Textorius, On generalized resolvents and Q-functions of symmetric linear relations, Pacific J. Math. 72 (1977), 135–165.
  • [11] M.M. Malamud, S.M. Malamud, Spectral theory of operator measures in a Hilbert space, Algebra i Analiz, 15 (2003), 1–77 [English translation: St. Petersburg Math. J. 15 (2004) 3, 323–373].
  • [12] B.Sz. Nagy, C. Foias, Harmonic analysis of operators on Hilbert space, North-Holland, Amsterdam, 1970.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH9-0004-0002
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