Doklady Mathematics

, Volume 92, Issue 2, pp 585–589 | Cite as

On the solvability of certain discrete equations and related estimates of discrete operators

  • A. V. Vasil’ev
  • V. B. Vasil’ev


The solvability of discrete equations with Calderón–Zygmund kernels is studied, the limit passage from the discrete to the continuous case is substantiated, and estimates of the errors of discrete solutions are obtained.


Half Space DOKLADY Mathematic Discrete Space Discrete Equation Discrete Solution 
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  1. 1.
    S. K. Abdullaev, Dokl. Akad. Nauk SSSR 292 (4), 777–779 (1987).MathSciNetGoogle Scholar
  2. 2.
    Gakhov, F.D., Boundary Value Problems (Nauka, Moscow, 1977) [in Russian].zbMATHGoogle Scholar
  3. 3.
    I. Ts. Gokhberg and I. A. Fel’dman, Equations in Convolutions and Projection Methods of Their Solution (Nauka, Moscow, 1971) [in Russian].Google Scholar
  4. 4.
    I. K. Daugavet, Theory of Approximate Methods: Linear Equations (BKhV-Peterburg, St. Petersburg, 2006) [in Russian].Google Scholar
  5. 5.
    S. G. Mikhlin, N. F. Morozov, and M. V. Paukshto, Integral Equations of Elasticity Theory (Izd. S.-Peterburg. Gos. Univ., St. Petersburg, 1994) [in Russian].Google Scholar
  6. 6.
    N. I. Muskhelishvili, Singular Integral Equations (Nauka, iMoscow, 1968) [in Russian].zbMATHGoogle Scholar
  7. 7.
    G. Nussbaumer, Fast Fourier Transform and Convolution Algorithms (Springer-Verlag, Berlin, 1982; Radio i Svyaz’, Moscow, 1982) [in Russian].CrossRefGoogle Scholar
  8. 8.
    S. L. Sobolev, Introduction to the Theory of Cubature Formulas (Nauka, iMoscow, 1974) [in Russian].Google Scholar
  9. 9.
    V. Z. Parton and P. I. Perlin, Methods of Mathematical Elasticity Theory (Nauka, iMoscow, 1981) [in Russian].zbMATHGoogle Scholar
  10. 10.
    S. G. Mikhlin and S. Prössdorf, Singular Integral Operators (Akademie-Verlag, iBerlin, 1986).CrossRefGoogle Scholar
  11. 11.
    P. Calderon, A. Bellow, C. Kenig, and P. Malliavin, Selected Papers of Alberto (Am. Math. Soc., Providence, R.I., 2008).zbMATHGoogle Scholar
  12. 12.
    A. V. Vasilyev and V. B. Vasilyev, Neural Paral. Sci. Comput. 20 (3/4), 313–326 (2012).zbMATHMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Belgorod National Research UniversityBelgorodRussia
  2. 2.Lipetsk State Technical UniversityLipetskRussia

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