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Approximation of analytic functions by polynomials with integer coefficients

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Abstract

For some classes of analytic functions we estimate the rate of approximation by polynomials with integer coefficients.

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References

  1. S. N. Mergelyan, “Representation of functions by series of polynomials on closed domains,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],78, No. 3, 405–408 (1951).

    MATH  MathSciNet  Google Scholar 

  2. S. Ya. Al'per, “Approximation of functions by polynomials with integer coefficients on closed domains,”Izv. Akad. Nauk SSSR, Ser. Mat. [Math. USSR-Izv.],28, No. 5, 1173–1186 (1964).

    MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  4. D. Gaier,Vorlesungen über Approximation in Komplexen, Birkhäuser Verlag, Basel-Boston-Stuttgart, 1980.

    Google Scholar 

  5. V. I. Belyi, “Conformal mappings and approximation of analytic functions in domains with quasiconformal boundary,”Mat. Sb. [Math. USSR-Sb.],102, No. 3, 331–361 (1977).

    MathSciNet  Google Scholar 

  6. R. M. Trigub, “Approximation of functions by polynomials with integer coefficients,”Izv. Akad. Nauk SSSR, Ser. Mat. [Math. USSR-Izv.],26, No. 2, 261–280 (1962).

    MATH  MathSciNet  Google Scholar 

  7. O. Ferguson,Approximation by Polynomials with Integral Coefficients, Amer. Math. Soc., Providence, R.I (1980).

    Google Scholar 

  8. I. E. Gopengauz, “About approximation of functions on a segment and on a domain with angles,” in:Function Theory, Functional Analysis, and their Applications [in Russian], Vol. 4, Khar'kov (1967), pp. 204–210.

    MATH  MathSciNet  Google Scholar 

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Translated fromMatematicheskie Zametki, Vol. 59, No. 2, pp. 182–188, February, 1996.

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Volchkov, V.V. Approximation of analytic functions by polynomials with integer coefficients. Math Notes 59, 128–132 (1996). https://doi.org/10.1007/BF02310951

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