Advertisement

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

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

Abstract

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.

References

  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

Personalised recommendations