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Approximation of the Classes B Ω p of Periodic Functions of Many Variables in Uniform Metric

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We obtain order estimates for the best M-term trigonometric approximations and approximations by Fourier sums for the classes B Ω p of periodic functions of many variables in the uniform metric.

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REFERENCES

  1. S. B. Stechkin, “On the absolute convergence of orthogonal series,” Dokl. Akad. Nauk SSSR, 102, No. 1 (1955).

    Google Scholar 

  2. R. S. Ismagilov, “Widths of sets in linear normed spaces and approximation of functions by trigonometric polynomials,” Usp. Mat. Nauk, 29, No. 3, 161–178 (1974).

    Google Scholar 

  3. V. E. Maiorov, “On linear widths of Sobolev classes,” Dokl. Akad. Nauk SSSR, 243, No. 5, 1127–1130 (1978).

    Google Scholar 

  4. Y. Makovoz, “On trigonometric n-widths and their generalizations,” J. Approxim. Theory, 41, No. 4, 361–366 (1984).

    Google Scholar 

  5. B. S. Kashin, “On approximation properties of complete orthonormal systems,” Tr. Mat. Inst. Akad. Nauk SSSR, 172, 187–192 (1985).

    Google Scholar 

  6. É. S. Belinskii, “Approximation by a ‘floating’ system of exponentials on classes of smooth periodic functions,” Mat. Sb., 132, No. 1, 20–27 (1987).

    Google Scholar 

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

    Google Scholar 

  9. É. S. Belinskii, “Approximation by a ‘floating’ system of exponentials on classes of periodic functions,” Tr. Mat. Inst. Akad. Nauk SSSR, 180, 46–47 (1987).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  12. A. S. Romanyuk, “The best trigonometric and bilinear approximations for functions of many variables from the classes B rp,θ .II,” Ukr. Mat. Zh., 45, No. 10, 1411–1423 (1993).

    Google Scholar 

  13. B. S. Kashin and V. N. Temlyakov, “On the best m-term approximations and the entropy of sets in the space L1,” Mat. Zametki, 56, No. 5, 57–86 (1994).

    Google Scholar 

  14. A. S. Romanyuk, “Best trigonometric and bilinear approximations for the Besov classes of functions of many variables,” Ukr. Mat. Zh., 47, No. 8, 1097–1111 (1995).

    Google Scholar 

  15. 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 

  16. S. Yongsheng and W. Heping, “Representation and approximation of multivariate periodic functions with bounded mixed moduli of smoothness,” Tr. Mat. Inst. Ross. Akad. Nauk, 219, 356–377 (1997).

    Google Scholar 

  17. S. A. Stasyuk, “Best M-term trigonometric approximations of the classes B Ωp,θ of functions of many variables,” Ukr. Mat. Zh., 54, No. 3, 381–394 (2002).

    Google Scholar 

  18. N. K. Bari and S. B. Stechkin, “Best approximations and differential properties of two conjugate functions,” Tr. Mosk. Mat. Obshch., 5, 483–522 (1956).

    Google Scholar 

  19. S. M. Nikol'skii, Approximation of Functions of Many Variables and Imbedding Theorems [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  20. N. N. Pustovoitov, “Representation and approximation of periodic functions of many variables with given modulus of continuity,” Anal. Math., 20, 35–48 (1994).

    Google Scholar 

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Stasyuk, S.A. Approximation of the Classes B Ω p of Periodic Functions of Many Variables in Uniform Metric. Ukrainian Mathematical Journal 54, 1885–1896 (2002). https://doi.org/10.1023/A:1024000709997

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