Advertisement

Siberian Mathematical Journal

, Volume 33, Issue 5, pp 914–922 | Cite as

On the Cauchy problem for holomorphic functions of Lebesgue classL2 in domains

  • A. A. Shlapunov
  • N. N. Tarkhanov
Article

Keywords

Cauchy Problem Holomorphic Function 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. M. Kytmanov, Bohner-Martinelli Integral and Its Applications [in Russian], Nauka, Novosibirsk (1991).Google Scholar
  2. 2.
    G. Zin, “Esistenza e reppresentazione di funzioni analitiche, le quali, su una curva di Jordan, si riducono a una funzioni assegnata,” Ann. Mat. Pura Appl.,34, 395–405 (1953).Google Scholar
  3. 3.
    D. I. Patil, “Representation ofH p-functions,” Bull. Amer. Math. Soc.,78, No. 4, 617–620 (1972).Google Scholar
  4. 4.
    M. G. Kreîn and P. Ya. Nudel'man, “On some new problems for the functions of Hardy class and continual families of functions with double orthogonality,” Dokl. Akad. Nauk SSSR,209, No. 3, 537–540 (1973).Google Scholar
  5. 5.
    A. Steiner, “Abschnitte von Randfunktionen beschränkter analytisher Funktionen,” Lecture Notes in Math,419, 342–540 (1973).Google Scholar
  6. 6.
    N. N. Tarkhanov, “A criterion of solvability of incorrect Cauchy problem for elliptic systems,” Dokl. Akad. Nauk SSSR,308, No. 3, 531–534 (1989).Google Scholar
  7. 7.
    L. A. Aîzenberg, “Possibility of analytic continuation into a domain of functions given on a boundary arc of the domain. The generalized Fock-Kuni theorem.,” in: Complex analysis and Mathematical Physics [in Russian], Krasnoyarsk (1988), pp. 5–11.Google Scholar
  8. 8.
    L. A. Aîzenberg and A. M. Kytmanov, Possibility of Holomorphic Continuation into a Domain of Functions Given on a Connected Part of the Boundary [in Russian], Preprint No. 50M., Institute of Physics, Krasnoyarsk (1988), pp. 5–11.Google Scholar
  9. 9.
    L. A. Aîzenberg, Carleman Formulas in Complex Analysis. First Applications [in Russian], Nauka, Novosibirsk (1990).Google Scholar
  10. 10.
    I. I. Privalov and I. P. Kuznetsov, “Boundary problems and various classes of harmonic functions defined in arbitrary domains,” Mat. Sb.,6, No. 3, 345–376 (1939).Google Scholar
  11. 11.
    I. I. Privalov, Boundary Properties of Analytic Functions [in Russian], Gostekhizdat, Moscow (1950).Google Scholar
  12. 12.
    E. Stein, Singular Integrals and Differentiability Properties of Functions [Russian translation], Mir, Moscow (1973).Google Scholar
  13. 13.
    G. M. Khenkin, “The method of integral representation in complex aalysis,” in: Itogi Nauki i Tekhniki. Fund. Naprav.,7, 23–124 (1985).Google Scholar
  14. 14.
    L. Hörmander, The Analysis of Linear Partial Differential Operators. Vol. 1: Distribution Theory and Fourier Analysis [Russian translation], Mir, Moscow (1986).Google Scholar
  15. 15.
    V. P. Mikhaîlov, Partial Differential Equations [in Russian], Nauka, Moscow (1976).Google Scholar
  16. 16.
    Functional Analysis [in Russian], Nauka, Moscow (1972).Google Scholar
  17. 17.
    I. F. Krasichkov, “The families of functions with double orthogonality,” Mat. Zametki,4, No. 5, 551–556 (1986).Google Scholar
  18. 18.
    R. Edwards, Functional Analysis. Theory and Applications [Russian translation], Mir, Moscow (1969).Google Scholar
  19. 19.
    T. Bagby, “Approximation in the mean by solutions of elliptic equations,” Trans. Amer. Math. Soc.281, No. 2, 701–784 (1984).Google Scholar
  20. 20.
    M. V. Keldysh and M. A. Lavrent'ev, “Sur les suites convergentes de polinomes harmoniques,” Trudy Tbiliss. Mat. Inst. Akad. Nauk Gruzin. SSR,1, 165–184 (1937).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • A. A. Shlapunov
  • N. N. Tarkhanov

There are no affiliations available

Personalised recommendations