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Characteristic Functions of Maximal Sectorial Operators

  • Conference paper

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 124))

Abstract

The analytic properties of the characteristic functions of maximal sectorial operators are studied and functional models are constructed.

Dedicated to Professor Israel Gohberg on the occasion of his 70-th birthday

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References

  1. Y.M. Arlinskii, Characteristic Functions of Operators of the Class C (α), Izv. Vuzov. Matematika no. 2 (1991), 13–21. (Russian)

    MathSciNet  Google Scholar 

  2. Y.M. Arlinskii, Extremal Extensions of Sectorial Linear Relations, Mat. Studii 7, no. 1 (1997), 81–96.

    MathSciNet  Google Scholar 

  3. Y.M. Arlinskii, On Functions Connected with Sectorial Operators and their Extensions, Int. Equat. Oper. Theory 33, no. 2 (1999), 125–152.

    Article  MathSciNet  MATH  Google Scholar 

  4. Y.M. Arlinskii, Positive Bounary Value Spaces and Sectorial Extensions of Non-negative Symmetric Operator, Ukrainian Math. Journ 40 no. 1 (1988), 8–15. (Russian)

    MathSciNet  Google Scholar 

  5. Y.M. Arlinskii, Maximal Sectorial Extensions and Associated with them Closed Forms, Ukrain. Math. Journ 48 no. 6 (1996), 723–738.

    MathSciNet  Google Scholar 

  6. Y.M. Arlinskii and E.R. Tsekanovskii, Regular Biextensions of Unbounded Operators, Donetsk University, Deposited in VINITI, N 2876–79 (1979), 73. (Russian)

    Google Scholar 

  7. Yu.M. Berezanskii, Expansions in eigenfunction of selfadjoint operators, Amer. Math. Soc. Providence 1968.

    Google Scholar 

  8. M.S. Brodskii, Triangular and Jordan representations of linear operators, Nauka, Moscow 1969. (Russian)

    Google Scholar 

  9. M.S. Brodskii and M.S. Livsic, Spectral Analysys of Nonself-Adjoint Operators and Intermediate Systems, Uspekhi Mat. Nauk 13 no. 1 (1958), 3–85. (Russian)

    MathSciNet  Google Scholar 

  10. D.N. Clark, On Model for Non-Contractions, Acta Sci. Math 36 (1974), 5–16.

    MATH  Google Scholar 

  11. V.A. Derkach and M.M. Malamud, Characteristic Functions of Almost Solvable Extensions of Hermitian Operators, Ukrainian Math. Journ 44 no. 4 (1992), 435–459. (Russian)

    MathSciNet  Google Scholar 

  12. V.A. Derkach and M.M. Malamud, Nonselfadjoint Extensions of an Hermitian Operator and their Characteristic Functions, J. Math. Sci 97, no. 5 (1999), 4420–1155.

    Article  MathSciNet  MATH  Google Scholar 

  13. V.A. Derkach, M.M. Malamud and E.R. Tsekanovskii, Sectorial Extensions of Positive Operator and a Characteristic Function, Ukrainian Mat. Journ 41, no. 2 (1989), 151–158. (Russian)

    MathSciNet  MATH  Google Scholar 

  14. P.A. Fillmore and J.P. Williams, On operator ranges, Advances in Math 7 (1971), 254–281.

    Article  MathSciNet  MATH  Google Scholar 

  15. I.S. Kac and M.G. Krein, R-functions — analityc functions mapping the upper half-plane into inself, Suplement Ito the Russian edition of F.V. Atkinson: Discrete and continuous boundary problems. Mir, Moscow 1968.

    Google Scholar 

  16. T. Kato, Perturbation theory for linear operators, Springer-Verlag, 1966.

    MATH  Google Scholar 

  17. A. Kuzhel, Characteristic functions and models of nonself-adjoint operators, Kluwer Academic Publishers. Dodrecht/Boston/London, 1996.

    Book  MATH  Google Scholar 

  18. M.G. Krein and H. Langer, Uber die Q-Function eines II-Hermiteschen Operators in Raum П k , Acta Sci. Math. Szeged 34 (1973), 191–230.

    MathSciNet  MATH  Google Scholar 

  19. M.S. Livsic, On a Spectral Decomposition of Linear Nonself-Adjoint Operators, Mat. Sbornik. 34 (1954), 144–199. (Russian)

    MathSciNet  Google Scholar 

  20. M.S. Livsic and A.A. Yantsevich, The theory of operator colligations in Hilbert spaces, Kharkov University, Kharkov, 1971. (Russian)

    Google Scholar 

  21. M.M. Malamud, On some Classes of Extensions of Hermitian Operators with Gaps, Ukrainian Math. Journ. 44 no. 2 (1992), 215–234. (Russian)

    Article  MathSciNet  Google Scholar 

  22. E.R. Tsekanovskii, Characteristic Function and Sectorial Boundary Problems, Trudy Inst. Mat. (Novosibirsk) Issled. Geom. Mat. Anal 7 (1987), 180–194. (Russian)

    MathSciNet  Google Scholar 

  23. E.R. Tsekanovskii, Triangular Models of Unbounded Accretive Operators and the Regular Factorization of their Characteristic Operator Functions, Dokl. Akad. Nauk USSR 297, no. 3 (1987), 552–556. (Russian)

    MathSciNet  Google Scholar 

  24. E.R. Tsekanovskii and Y.L. Shmulyan, The Theory of Biextensions of Operators in Hilbert Spaces, Uspekhi Mat. Nauk 32, no. 5 (1977), 69–124. (Russian)

    Google Scholar 

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Arlinskii, Y. (2001). Characteristic Functions of Maximal Sectorial Operators. In: Dijksma, A., Kaashoek, M.A., Ran, A.C.M. (eds) Recent Advances in Operator Theory. Operator Theory: Advances and Applications, vol 124. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8323-8_4

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  • DOI: https://doi.org/10.1007/978-3-0348-8323-8_4

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9516-3

  • Online ISBN: 978-3-0348-8323-8

  • eBook Packages: Springer Book Archive

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