The General Form of Maximally Accretive Quasi-differential Operators for First Order

  • Pembe Ipek
  • Zameddin I. Ismailov
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 24)


In this work, firstly all maximally accretive extensions of the minimal operator generated by first-order linear symmetric multipoint quasi-differential operator expression in the direct sum of weighted Hilbert spaces of vector-functions defined at the left and right semi-infinite intervals are described. Later on, the structure of spectrum of such extensions is investigated.


  1. 1.
    Bairamov, E., Öztürk Mert, R., Ismailov, Z.: Selfadjoint extensions of a singular differential operator. J. Math. Chem. 50, 1100–1110 (2012)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bairamov, E., Sertbaş, M., Ismailov, Z.: Self-adjoint extensions of singular third-order differential operator and applications. AIP Conf. Proc. 1611, 177–182 (2014)CrossRefGoogle Scholar
  3. 3.
    Gorbachuk, V.I., Gorbachuk, M.L.: Boundary Value Problems for Operator Differential Equations. Kluwer Academic Publisher, Dordrecht (1991)CrossRefGoogle Scholar
  4. 4.
    Hörmander, L.: On the theory of general partial differential operators. Acta Math. 94, 161–248 (1955)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Ismailov, Z.I., Sertbaş, M., Otkun Çevik, E.: Selfadjoint extensions of a first order differential operator. Appl. Math. Inf. Sci Lett. 3(2), 39–45 (2015)Google Scholar
  6. 6.
    Kato, T.: Perturbation Theory for Linear Operators. Springer, New York (1966)zbMATHGoogle Scholar
  7. 7.
    Levchuk, V.V.: Smooth maximally dissipative boundary-value problems for a parabolic equation in a Hilbert space. Ukr. Math. J. 35(4), 502–507 (1983)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Rofe-Beketov, F.S., Kholkin, A.M.: Spectral Analysis of Differential Operators. World Scientific Monograph Series in Mathematics, vol. 7. World Scientific, Hackensack (2005)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Pembe Ipek
    • 1
  • Zameddin I. Ismailov
    • 2
  1. 1.Institute of Natural SciencesKaradeniz Technical UniversityTrabzonTurkey
  2. 2.Department of MathematicsKaradeniz Technical UniversityTrabzonTurkey

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