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Ukrainian Mathematical Journal

, Volume 62, Issue 6, pp 928–942 | Cite as

On solutions of one class of second-order operator differential equations in the class of holomorphic vector functions

  • S. S. Mirzoev
  • S. G. Veliev
Article

We establish sufficient conditions for the completeness of a part of root vectors of one class of the second-order operator bundles corresponding to the characteristic numbers from a certain sector and prove the theorem on completeness of a system of elementary holomorphic solutions of the corresponding second-order homogeneous operator differential equations. We also indicate the conditions of correct and unique solvability of a boundary-value problem for the analyzed equation with linear operator in the boundary condition and estimate the norm of the operator of the intermediate derivative in the perturbed part of the equation.

Keywords

Hilbert Space Vector Function Elementary Solution Regular Solution Characteristic Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • S. S. Mirzoev
    • 1
  • S. G. Veliev
    • 1
  1. 1.Baku State UniversityBakuAzerbaijan

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