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Number of integral points in a certain set and the approximation of functions of several variables

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Literature cited

  1. V. M. Tikhomirov, Some Questions in Approximation Theory [in Russian], Moscow State Univ. (1976).

  2. K. I. Babenko, “Approximation of periodic functions of several variables by trigonometric polynomials,” Dokl. Akad. Nauk SSSR,132, No. 2, 247–250 (1960).

    Google Scholar 

  3. K. I. Babenko, “Approximation of a certain class of periodic functions of several variables by trigonometric polynomials, Dokl. Akad. Nauk SSSR,132, No. 5, 982–985 (1960).

    Google Scholar 

  4. S. A. Telyakovskii, “Certain estimates for trigonometric series with quasiconvex coefficients,” Mat. Sb.,63, No. 3, 426–444 (1964).

    Google Scholar 

  5. N. S. Nikol'skaya, “Approximation of differentiable functions of several variables by Fourier sums in the Lp metric,” Dokl. Akad. Nauk SSSR,208, No. 6, 1282–1285 (1973).

    Google Scholar 

  6. E. M. Galeev, “Approximation of classes of functions with several bounded derivatives by Fourier sums,” Mat. Zametki,23, No. 2, 197–212 (1978).

    Google Scholar 

  7. E. M. Galeev, “Approximation of classes of functions with several bounded derivatives,” Candidate's Dissertation, Moscow State Univ. (1978).

  8. Din' Zung and G. G. Magaril-Il'yaev, “Bernshtein- and Favard-type problems and the mean ɛ-dimension of some classes of functions,” Dokl. Akad. Nauk SSSR,249, No. 4, 783–786 (1979).

    Google Scholar 

  9. Din' Zung, “On certain approximative characteristics of classes of smooth functions of several variables in the ℒ2 metric,” Usp. Mat. Nauk,34, No. 4, 189–190 (1979).

    Google Scholar 

  10. R. T. Rockafellar, Convex Analysis, Princeton Univ. Press (1970).

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Translated from Matematicheskie Zametki, Vol. 36, No. 4, pp. 479–491, October, 1984.

The author expresses his sincere gratitude to V. M. Tikhomirov for the formulation of the problem and for his constant interest.

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Zung, D. Number of integral points in a certain set and the approximation of functions of several variables. Mathematical Notes of the Academy of Sciences of the USSR 36, 736–744 (1984). https://doi.org/10.1007/BF01156461

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