Ukrainian Mathematical Journal

, Volume 29, Issue 6, pp 578–581 | Cite as

The Cauchy problem for parabolic equations with essentially infinite-dimensional elliptic operators

  • Yu. V. Bogdanskii
Brief Communications


Cauchy Problem Parabolic Equation Elliptic Operator 
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.
    P. Levi, Concrete Problems of Functional Analysis [in Russian], Nauka, Moscow (1967).Google Scholar
  2. 2.
    G. E. Shilov, “On some problems in analysis in Hilbert space. 1,” Funkts. Anal. Prilozhen.,1, No. 2, 81–90 (1967).Google Scholar
  3. 3.
    G. E. Shilov, “On some problems in analysis in Hilbert space. 2,” Mat. Issled.,2, No. 4, 166–186 (1967).Google Scholar
  4. 4.
    G. E. Shilov, “On some problems in analysis in Hilbert space. 3,” Mat. Sb.,74, No. 1, 161–168 (1967).Google Scholar
  5. 5.
    A. S. Nemirovskii and G. E. Shilov, “On an axiomatic description of the Laplace operator for functions on a Hilbert space,” Funkts. Anal. Prilozhen.,3, No. 3, 79–85 (1969).Google Scholar
  6. 6.
    I. Ya. Dorfman, “On the means and the Laplacian of functions on Hilbert space,” Mat. Sb.,81, No. 2, 192–208 (1970).Google Scholar
  7. 7.
    Yu. V. Bogdanskii, “On a class of second-order differential operators for functions of infinite-dimensional argument,” Dopov. Akad. Nauk UkrSSR, Ser. A, No. 1, 6–9 (1977).Google Scholar
  8. 8.
    M. A. Naimark, Normed Rings [in Russian], Nauka, Moscow (1968).Google Scholar
  9. 9.
    V. Ya. Sikiryavyi, “A quasidifferentiation operator and boundary problems associated with it,” Tr. Mosk. Mat. O-va,27, 195–246 (1972).Google Scholar
  10. 10.
    E. M. Polishchuk, “On functional analogs of the heat-conduction equation,” Sib. Mat. Zh.,6, No. 6, 1322–1331 (1965).Google Scholar
  11. 11.
    I. Ya. Dorfman, “On the heat-conduction equation in Hilbert space,” Vestn. Mosk. Gos. Univ., No. 4, 46–51 (1971).Google Scholar
  12. 12.
    Yu. L. Daletskii and N. M. Kukharchuk, “First-order equations with functional derivatives,” Ukr. Mat. Zh.,17, No. 6, 114–117 (1965).Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • Yu. V. Bogdanskii
    • 1
  1. 1.Kiev Polytechnic InstituteUSSR

Personalised recommendations