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Approximation of Classes B r p,θ by Linear Methods and Best Approximations

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Ukrainian Mathematical Journal Aims and scope

Abstract

We investigate problems related to the approximation by linear methods and the best approximations of the classes \(B_{p,{\theta }}^r\), 1 ≤ p ≤ ∞ in the space L ∞.

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REFERENCES

  1. S. M. Nikol'skii, Approximation of Functions of Many Variables and Imbedding Theorems [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  2. V. N. Temlyakov, “Approximation of functions with bounded mixed derivative,” Tr. Mat. Inst. Akad. Nauk SSSR, 178, 1–112 (1986).

    Google Scholar 

  3. W. Dahmen and E. Gorlich, “A conjecture of M. Golomb on optimal and nearly-optimal approximation,” Bull. Amer. Math. Soc., 80, No. 6, 1199–1202 (1974).

    Google Scholar 

  4. V. N. Temlyakov, “Approximation of functions with bounded mixed difference by trigonometric polynomials and widths of certain classes of functions,” Izv. Akad. Nauk SSSR, Ser. Mat., 46, No. 1, 171–186 (1982).

    Google Scholar 

  5. V. N. Temlyakov, “Approximation of periodic functions of several variables by trigonometric polynomials and widths of certain classes of functions,” Izv. Akad. Nauk SSSR, Ser. Mat., 49, No. 5, 986–1030 (1985).

    Google Scholar 

  6. S. M. Nikol'skii, “Inequalities for entire functions of finite order and their application to the theory of differentiable functions of many variables,” Tr. Mat. Inst. Akad. Nauk SSSR, 38, 244–278 (1951).

    Google Scholar 

  7. D. Jackson, “Certain problem of closest approximation,” Bull. Amer. Math. Soc., 39, No. 12, 889–906 (1933).

    Google Scholar 

  8. J. Marcinkiewicz, “Quelques remarques sur l'interpolation,” Acta Litt. Acad. Sci. Szeged, 8, 127–130 (1937).

    Google Scholar 

  9. A. S. Romanyuk, “On estimates for approximation characteristics of the Besov classes of periodic functions of many variables,” Ukr. Mat. Zh., 49, No. 9, 1250–1261 (1997).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    A. S. Romanyuk

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  1. A. S. Romanyuk
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Romanyuk, A.S. Approximation of Classes B r p,θ by Linear Methods and Best Approximations. Ukrainian Mathematical Journal 54, 825–838 (2002). https://doi.org/10.1023/A:1021691615557

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