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Ukrainian Mathematical Journal

, Volume 65, Issue 5, pp 780–786 | Cite as

Linear Combinations of the Volterra Dissipative Operator and Its Adjoint Operator

  • G. M. Gubreev
  • E. I. Olefir
  • A. A. Tarasenko
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We study the spectral properties of linear combinations of the Volterra dissipative operator and its adjoint operator in a separable Hilbert space.

Keywords

Adjoint Operator Separable Hilbert Space Volterra Operator Muckenhoupt Weight Root Subspace 
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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References

  1. 1.
    I. Ts. Gokhberg and M. G. Krein, Introduction to the Theory of Linear Nonself-Adjoint Operators in a Hilbert Space [in Russian], Nauka, Moscow (1965).Google Scholar
  2. 2.
    I. Ts. Gokhberg and M. G. Krein, Theory of Volterra Operators in a Hilbert Space and Its Applications [in Russian], Nauka, Moscow (1967).Google Scholar
  3. 3.
    G. M. Gubreev and Yu. D. Latushkin, “Functional models of nonself-adjoint operators, strongly continuous semigroups, and matrix Muckenhoupt weights,” Izv. Ros. Akad. Nauk, Ser. Mat., 75, No. 2, 69–126 (2011).MathSciNetCrossRefGoogle Scholar
  4. 4.
    G. M. Gubreev and A. A. Tarasenko, “Criterion of unconditional basis property for the eigenvectors of finite-dimensional perturbations of Volterra operators,” Funkts. Anal. Prilozhen., 45, No. 2, 86–91 (2011).MathSciNetCrossRefGoogle Scholar
  5. 5.
    M. S. Brodskii, Triangular and Jordan Representations of Linear Operators [in Russian], Nauka, Moscow (1969).Google Scholar
  6. 6.
    J. B. Garnett, Bounded Analytic Functions, Academic Press, New York (1981).zbMATHGoogle Scholar
  7. 7.
    M. S. Brodskii and M. S. Lifshits, “Spectral analysis of nonself-adjoint operators and intermediate systems,” Usp. Mat. Nauk, 13, No. 1, 3–85 (1958).Google Scholar
  8. 8.
    Yu. P. Ginzburg, “On almost invariant spectral properties of compressions and multiplicative properties of analytic operator functions,” Funkts. Anal. Prilozhen., 5, No. 3, 32–41 (1971).MathSciNetGoogle Scholar
  9. 9.
    N. K. Nikol’skii, Lectures on the Translation Operator [in Russian], Nauka, Moscow (1980).Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • G. M. Gubreev
    • 1
  • E. I. Olefir
    • 2
  • A. A. Tarasenko
    • 3
  1. 1.Poltava National Technical UniversityPoltavaUkraine
  2. 2.Odessa National Pedagogic UniversityOdessaUkraine
  3. 3.Autonomous University of Hidalgo StatePachucaMexico

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