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On best approximation of infinitely differentiable functions

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Literature Cited

  1. S. N. Bernshtein, “On the approximation of continuous functions by polynomials,” in: Collected Works, Academy of Sciences of the USSR, Vol. 1 [in Russian] (1952), pp. 8–10.

  2. J. R. Rice, The Approximation of Functions, Addison-Wesley (1964).

  3. M. S. Baouendi and C. Coulaoic, “Approximation polynomiale de fonctions C et analytiques,” Ann. Inst. Fourier (Grenoble),21, No. 4, 149–173 (1971).

    Google Scholar 

  4. A. F. Timan, Theory of Approximations of Fucntions of a Real Variable [in Russian], Fizmatgiz, Moscow (1960).

    Google Scholar 

  5. P. L. Ul'yanov, “On classes of infinitely differentiable functions,” Dokl. Akad. Nauk SSSR,305, No. 2, 287–290 (1989).

    Google Scholar 

  6. Yu. A. Brudnyi and I. E. Gopengauz, “Approximation by piecewise-polynomial functions,” Izv. Akad. Nauk SSSR, Ser. Mat.,27, No. 4, 723–746 (1963).

    Google Scholar 

  7. K. I. Babenko, “On some problems of the theory of approximations and numerical analysis,” Usp. Mat. Nauk,40, No. 1, 3–27 (1985).

    Google Scholar 

  8. M. I. Ganzburg, “On best approximation of infinitely differentiable functions,” in: Theory of Approximation of Functions, All-Union Symposium, August 31-September 8, Lutsk (1989), Thesis Reports, Inst. of Math., Acad. of Sciences of the Ukrainian SSR (1989), pp. 46–47.

  9. P. L. Butzer and R. L. Stens, “Chebyshev transform methods in the theory of best algebraic approximation,” Abh. Math. Sem. Univ. Hamburg,45, 165–190 (1976).

    Google Scholar 

  10. M. D. Sterlin, “Estimates of constants in inverse theorems of the constructive theory of functions,” Dokl. Akad. Nauk SSSR,209, No. 6, 1296–1298 (1973).

    Google Scholar 

  11. N. I. Akhiezer, Lectures on the Theory of Approximation [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  12. S. Mandelbrojt, Adherent Series. Regularization of Sequences. Applications [Russian translation], Moscow (1955).

  13. E. Seneta, Properly Varying Functions [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  14. M. V. Fedoryuk, Asymptotics: Integrals and Series [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  15. L. Hörmander, Analysis of Linear Partial Differential Operators, Vol. 1: Theory of Distributions and Fourier Analysis [Russian translation], Mir, Moscow (1986).

    Google Scholar 

  16. H. Bateman and A. Erdelyi, Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York (1954).

    Google Scholar 

  17. G. Szegö, Orthogonal Polynomials, Colloquium Publications, Vol. 23, Am. Math. Soc., Providence (1959).

    Google Scholar 

  18. H. F. Sinwel, “Uniform approximation of differentiable functions by algebraic polynomials,” J. Approx. Theory,32, No. 1, 1–8 (1981).

    Google Scholar 

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Dnepropetrovsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 5, pp. 12–28, September–October, 1991.

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Ganzburg, M.I. On best approximation of infinitely differentiable functions. Sib Math J 32, 733–749 (1991). https://doi.org/10.1007/BF00971172

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  • DOI: https://doi.org/10.1007/BF00971172

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