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Direct methods for the approximate solution of operator equations with nonzero kernel

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Abstract

We justify direct methods for the approximate solution of linear operator equations with nonzero kernels and apply these methods to the justification of projective methods for the approximate solution of standard singular integral equations with Cauchy kernels and positive index on the unit disk.

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References

  1. R. E. Edwards, Functional Analysis: Theory and Approximations, Holt, Rinehart & Winston (1965).

    Google Scholar 

  2. L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  3. V. A. Trenogin, Functional Analysis [in Russian], Nauka, Moscow (1980).

    MATH  Google Scholar 

  4. V. V. Ivanov, Theory of Approximation Methods and Its Application to the Numerical Solution of Singular Integral Equations [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  5. B. I. Gabdulkhaev, Optimum Approximations of Solutions of Linear Problems [in Russian], Kazan University, Kazan (1980).

    Google Scholar 

  6. Z. Presdorff, Some Classes of Singular Equations [Russian translation], Mir, Moscow (1979).

    Google Scholar 

  7. G. M. Vainikko, Compact Approximation of Operators and the Approximate Solution of Equations [in Russian], Tartu, Tartu University (1970).

    Google Scholar 

  8. M. A. Krasnosel’skii, G. M. Vainikko, P. P. Zabreiko, Ya. V. Rutitskii, and V. Ya. Stetsenko, Approximate Solution of Operator Equations [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  9. Yu. A. Cherskii, “Two theorems on error estimates and some applications,” Dokl. Akad. Nauk SSSR, 150, No. 2, 271–274 (1963).

    MathSciNet  Google Scholar 

  10. N. Ya. Tikhonenko, “On the method of approximate factorization,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 4, 74–86 (1976).

  11. F. D. Gakhov, Boundary-Value Problems [in Russian], Nauka, Moscow (1977).

    MATH  Google Scholar 

  12. N. P. Korneichuk, Exact Constants in the Theory of Approximation [in Russian], Nauka, Moscow (1987).

    Google Scholar 

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Authors and Affiliations

  1. Odessa University, Odessa

    K. I. Malyshev & N. Ya. Tikhonenko

Authors
  1. K. I. Malyshev
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  2. N. Ya. Tikhonenko
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 9, pp. 1202–1213, September, 1998.

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Malyshev, K.I., Tikhonenko, N.Y. Direct methods for the approximate solution of operator equations with nonzero kernel. Ukr Math J 50, 1376–1388 (1998). https://doi.org/10.1007/BF02525244

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  • DOI: https://doi.org/10.1007/BF02525244

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