Skip to main content
SpringerLink
Log in

On convergence of the method of approximate factorization. I

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. V. A. Babenko, “On one effective method for solution of certain integral equations in the theory of elasticity and mathematical physics”, Prikl. Mat. Mekh.31, No. 1, 80–89 (1976).

    Google Scholar 

  2. B. Noble,The Wiener-Hopf Method [Russian translation], IIL, Moscow (1962).

    Google Scholar 

  3. G. Ya. Popov,Contact Problems for Linearly Deformable Bases [in Russian], Visha Shkola, Kiev-Odessa (1982).

    Google Scholar 

  4. G. Ya. Popov, “Toward solution of problems in the theory of elasticity with the method of factorization”, Prikl. Mat. Mekh.,38, No. 1, 178–183 (1974).

    MATH  Google Scholar 

  5. G. Ya. Popov, andA.A. Paskalenko, “The plane problem on bending infinite cylinders on linearly deformable bases”, Prikl. Mat. Mekh.,36, No. 1, 178–183 (1972).

    Google Scholar 

  6. Yu. I. Cherskii, “Problems in mathematical physics that reduce to the Riemann problem”, Tr. Mat. Inst. Akad. Nauk Gruz SSR,28, 209–246 (1961).

    Google Scholar 

  7. F. D. Gakhov andYu. I. Cherskii,Equations for Convolutions [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  8. M. G. Krein, “Integral equations on the half-line with kernels that depend on the differences of arguments”, Usp. Mat. Nauk,13, No. 5, 3–120 (1958).

    MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  10. G. N. Pykhteev,Exact Methods for Evaluating Integrals of Cauchy Type [in Russian], Nauka, Novosibirsk (1980).

    Google Scholar 

  11. Yu. I. Cherskii, “Two theorems on error estimation and some of their applications”, Dokl. Akad. Nauk SSSR,150, No. 2, 271–274 (1963).

    MATH  MathSciNet  Google Scholar 

  12. Yu. I. Cherskii, “Toward solution of mixed problems for partial differential equations”, Differents. Uravn.,1 No. 5, 647–662 (1965).

    MATH  Google Scholar 

  13. Yu. I. Cherskii, “Approximate solution of Wiener-Hopf equations in one special case”, Differents. Uravn.,2, No. 6, 1093–1100 (1966).

    MATH  Google Scholar 

  14. N. Ya. Tikhonenko, “Toward approximate solution of a special case of the Riemann problem in the theory of analytic functions”, Teoriya Funktsii, Funk. Analiz i Ikh Prilozh., No. 10, 27–35 (1970).

    MATH  Google Scholar 

  15. I. Ya. Tikhonenko, “The method of approximate factorization”, Izv. Vuzov Mat., No. 4, 74–86 (1976).

    MATH  Google Scholar 

  16. V. V. Ivanov,The Theory of Integral Equations [in Russian], Naukova Dumka, Kiev (1968).

    Google Scholar 

  17. V. I. Kas'yanov, “Rational approximation of integrals of Cauchy type and approximate solution of the Riemann problem for the half-plane”, Izv. Vuzov. Mat., No. 11, 50–55 (1981).

    Google Scholar 

  18. G. Yu. Vinogradova, “Singular integral operators on an axis with a fractional linear translation in a weighted space”, Izv. Vurov Mat., No. 3, 67–72 (1979).

    MATH  MathSciNet  Google Scholar 

  19. V. N. Rusak,Rational Functions as an Apparatus for Approximating Rational Functions on the Real Axis [in Russian], Izd. BGU, Minsk (1979).

    Google Scholar 

  20. V. N. Rusak, “One method for approximating rational functionals on the real axis”, Mat. Zamet.,22, No. 3, 375–380 (1977).

    MATH  MathSciNet  Google Scholar 

  21. A. P. Svetnoi andN. Ya. Tikhonenko, “On approximate solution of the Riemann boundary-varlue problem with discontinuous coefficients and right side”, Zh. Vychisl. Mat. Mat. Fiz.,22, No. 2, 128–136 (1982).

    MathSciNet  Google Scholar 

  22. N. P. Korneichuk, A. A. Ligun, andV. G. Doronin,Approximations With Constraints [in Russian], Naukova Dumka, Kiev (1982).

    Google Scholar 

  23. W. T. Koiter, “Approximate solution of Wiener-Hopt type integral equations with applications, I”, Konike. Ned. Akad. Weteushap. Proc.,57, 552–579 (1954).

    Google Scholar 

Download references

Authors
  1. Baza Khedidzha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Ya. Tikhonenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromTeoriya Funktsii, Funktsional'nyi Analiz, i Ikh Prilozheniya, Vol. 58, pp. 106–120, 1993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khedidzha, B., Tikhonenko, N.Y. On convergence of the method of approximate factorization. I. J Math Sci 85, 2224–2234 (1997). https://doi.org/10.1007/BF02355774

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02355774

Keywords

Search

Navigation