Skip to main content
Log in

Approximation of functions of several variables by polynomials with preservation of the differential-difference properties

  • Published:
Ukrainian Mathematical Journal Aims and scope

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

Access this article

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

Instant access to the full article PDF.

Literature cited

  1. S. M. Nikol'skii, Approximation of Functions of Several Variables and Embedding Theorems [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  2. S. B. Stechkin, “On the order of best approximation of continuous functions,” Izv. Akad. Nauk SSSR, Ser. Mat.,15, No. 3, 219–242 (1951).

    Google Scholar 

  3. A. F. Timan, Theory of Approximation of Functions of a Real Variable [in Russian], Fizmatgiz, Moscow (1960).

    Google Scholar 

  4. V. K. Dzyadyk, Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  5. Yu. A. Brudnyi, “Approximation of functions defined in a convex polyhedron,” Dokl. Akad. Nauk SSSR,190, No. 2, 9–11.

  6. O. V. Besov, “Continuation of functions outside a region with preservation of differential-difference properties in Lp,” Mat. Sb.,66, No. 1, 80–96 (1965).

    Google Scholar 

  7. Yu. A. Brudnyi, “Continuation of a function with preservation of order of decrease of continuity moduli,” in: Studies in the Theory of Functions of Several Real Variables, No. 2, 33–69, Yaroslav Univ. (1978).

  8. V. N. Konovalov, “Differential properties and approximation of functions of several variables,” Preprint 79.21, Inst. Math. Acad. Sci. Ukr. SSR, Kiev (1979).

    Google Scholar 

  9. V. N. Konovalov, “A Jackson-type approximation theorem for functions of several variables,” Ukr. Mat. Zh.,33, No. 6, 757–764 (1981).

    Google Scholar 

  10. Yu. A. Brudnyi, “On a theorem of local best approximations,” Uch. Zap. Kazansk. Univ., No. 6, 43–49 (1964).

    Google Scholar 

  11. V. I. Burenkov, “Sobolev's integral representation and Taylor's formula,” Tr. Mat. Inst. Akad. Nauk SSSR,131, 33–38 (1973).

    Google Scholar 

  12. V. N. Konovalov, “Connection between differential-difference properties of a function and entire functions of exponential type that are approximating it,” in: Problems of the Theory of Approximation of Functions and Its Applications, Inst. Math. Acad. Sci. Ukr. SSR, Kiev (1976), pp. 116–123.

    Google Scholar 

  13. M. I. Ganzburg, “Some inequalities for polynomials and entire functions of finite degree in symmetric spaces,” in: Theory of Approximation of Functions [in Russian], Nauka, Moscow (1977), pp. 104–107.

    Google Scholar 

  14. S. M. Nikol'skii, “A method for covering a region, and inequalities for polynomials of several variables,” Mathematica (Rumania, Cluj),8, No. 2, 345–356 (1966).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 36, No. 2, pp. 154–160, March–April, 1984.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Konovalov, V.N. Approximation of functions of several variables by polynomials with preservation of the differential-difference properties. Ukr Math J 36, 138–143 (1984). https://doi.org/10.1007/BF01066944

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01066944

Navigation