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On the Cauchy problem for holomorphic functions of Lebesgue classL 2 in domains

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References

  1. A. M. Kytmanov, Bohner-Martinelli Integral and Its Applications [in Russian], Nauka, Novosibirsk (1991).

    Google Scholar 

  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. D. I. Patil, “Representation ofH p-functions,” Bull. Amer. Math. Soc.,78, No. 4, 617–620 (1972).

    Google Scholar 

  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. A. Steiner, “Abschnitte von Randfunktionen beschränkter analytisher Funktionen,” Lecture Notes in Math,419, 342–540 (1973).

    Google Scholar 

  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. 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.

  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. L. A. Aîzenberg, Carleman Formulas in Complex Analysis. First Applications [in Russian], Nauka, Novosibirsk (1990).

    Google Scholar 

  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. I. I. Privalov, Boundary Properties of Analytic Functions [in Russian], Gostekhizdat, Moscow (1950).

    Google Scholar 

  12. E. Stein, Singular Integrals and Differentiability Properties of Functions [Russian translation], Mir, Moscow (1973).

    Google Scholar 

  13. G. M. Khenkin, “The method of integral representation in complex aalysis,” in: Itogi Nauki i Tekhniki. Fund. Naprav.,7, 23–124 (1985).

  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. V. P. Mikhaîlov, Partial Differential Equations [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  16. Functional Analysis [in Russian], Nauka, Moscow (1972).

  17. I. F. Krasichkov, “The families of functions with double orthogonality,” Mat. Zametki,4, No. 5, 551–556 (1986).

    Google Scholar 

  18. R. Edwards, Functional Analysis. Theory and Applications [Russian translation], Mir, Moscow (1969).

    Google Scholar 

  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. 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 

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Krasnoyarsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 33, No. 5, pp. 186–195, September–October, 1992.

Translated by N. S. Dairbekov

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Shlapunov, A.A., Tarkhanov, N.N. On the Cauchy problem for holomorphic functions of Lebesgue classL 2 in domains. Sib Math J 33, 914–922 (1992). https://doi.org/10.1007/BF00970999

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  • DOI: https://doi.org/10.1007/BF00970999

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