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Best trigonometric and bilinear approximations for the Besov classes of functions of many variables

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Abstract

We obtain order estimates for the best trigonometric and bilinear approximations for the classesB r p,θ of functions of many variables.

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References

  1. A. S. Romanyuk, “The best trigonometric and bilinear approximations of functions of many variables from the classesB r p,θ . I,”Ukr. Mat. Zh.,44, No. 11, 1535–1547 (1992).

    Google Scholar 

  2. A. S. Romanyuk, “The best trigonometric approximations and the Kolmogorov diameters of the Besov classes of functions of many variables,”Ukr. Mat. Zh.,45, No. 5, 663–675 (1993).

    Google Scholar 

  3. A. S. Romanyuk, “The best trigonometric and bilinear approximations of functions of many variables from the classesB r p,θ . II,”Ukr. Mat. Zh.,45, No. 10, 1411–1423 (1993).

    Google Scholar 

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

    Google Scholar 

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

  6. A. S. Romanyuk, “On the best approximations and Kolmogorov widths of Besov classes of periodic functions of many variables,”Ukr. Mat. Zh.,47, No. 1, 79–92 (1995).

    Google Scholar 

  7. É. S. Belinskii, “Approximation of functions of many variables by a ‘floating’ system of exponentials and trigonometric widths,”Dokl. Akad. Nauk SSSR,284, No. 6, 1294–1297 (1985).

    Google Scholar 

  8. A. S. Romanyuk, “Approximation of Besov classes of periodic functions of many variables in the space Lq,”Ukr. Mat. Zh.,43, No. 10, 1398–1408 (1991).

    Google Scholar 

  9. É. S. Belinskii, “Approximation of functions of several variables by trigonometric polynomials with given number of harmonics, and estimates of ɛ-entropy,”Anal. Math.,15, No. 2, 67–74 (1989).

    Google Scholar 

  10. V. N. Temlyakov, “The approximation of periodic functions of many variables by combinations of functions that depend on fewer variables,”Tr. Inst. Mat. Akad. Nauk SSSR,173, 243–252 (1986).

    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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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 8, pp. 1097–1111, August, 1995.

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Romanyuk, A.S. Best trigonometric and bilinear approximations for the Besov classes of functions of many variables. Ukr Math J 47, 1253–1270 (1995). https://doi.org/10.1007/BF01057714

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  • DOI: https://doi.org/10.1007/BF01057714

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