The Existence of Solutions of Linear Hamiltonian Equations with Unbounded Operators

  • V. I. Derguzov
  • V. A. Yakubovich
Part of the Problems in Mathematical Analysis / Problemy Matematicheskogo Analiza / Πроблемы Математического Анализа book series (PMA)


The present article is devoted to a proof of the existence of solutions of the linear Hamiltonian equation
$$ J\frac{{dx}}{{dt}} = H\left( t \right)x\left( {H\left( {t + \tau } \right) = H\left( t \right)} \right) $$
in a complex separable Hilbert space. Here, J is a symmetric anti-Hermitian operator that is bounded together with its inverse and H(t) is an unbounded operator that, generally speaking, is self-adjoint and close in a definite sense to a positive definite operator.*


Generalize Solution Integral Identity Hamiltonian Equation Unbounded Operator Operator Differential Equation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    Yu. L. Daletskii, Uspekhi Matem. Nauk, Vol. 17, No. 5 (107) (1962).MathSciNetGoogle Scholar
  2. 2.
    V. V. Nemytskii, M. M. Vainberg, and R. S. Gusarova, Progress in Mathematics: Mathematical Analysis [in Russian] (1964 and 1965).Google Scholar
  3. 3.
    V. I. Derguzov and V. A. Yakubovich, Dokl. Akad. Nauk SSSR, Vol. 151, No. 6 (1963).Google Scholar
  4. 4.
    T. Kato, “Integration of the equation of evolution in Banach space,” J. Math. Soc. Japan, Vol.5 (1953).Google Scholar
  5. 5.
    O. A. Ladyzhenskaya, Matem. Sbornik, Vol. 39 (81), No. 4 (1956).MathSciNetGoogle Scholar
  6. 6.
    M. I. Vishik, Matem. Sbornik, Vol. 39 (81), No. 1 (1956).Google Scholar
  7. 7.
    E. Hille and R. Phillips, Functional Analysis and Semigroups [Russian translation], Izd. “Mir,” Moscow (1962).Google Scholar
  8. 8.
    L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces [in Russian], GIFML, Moscow-Leningrad (1959).Google Scholar
  9. 9.
    V. I. Derguzov, Matem. Sbornik, Vol. 63 (105), No. 4 (1964).MathSciNetGoogle Scholar
  10. 10.
    V. A. Yakubov, Vestnik Leningradsk. Gos. Univ., No. 12, Issue 3 (1958).Google Scholar

Copyright information

© Consultants Bureau, New York 1971

Authors and Affiliations

  • V. I. Derguzov
  • V. A. Yakubovich

There are no affiliations available

Personalised recommendations