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Trigonometric Widths of the Classes B Ω p of Periodic Functions of Many Variables

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Abstract

We obtain exact order estimates for the trigonometric widths of the classes \(B_{p,{\theta }}^\Omega\) of periodic functions of many variables in the space L q, 1 < p ≤ 2 ≤ q < p/(p − 1).

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REFERENCES

  1. 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 

  2. V. E. Maiorov, “On linear widths of Sobolev classes and chains of extremal spaces,” Mat. Sb., 113, No. 3, 437–463 (1980).

    Google Scholar 

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

    Google Scholar 

  4. É. S. Belinskii, “Approximation of periodic functions by a “floating” system of exponentials and trigonometric widths],” in: Investigations in the Theory of Functions of Many Real Variables [in Russian], Yaroslavl University, Yaroslavl (1984), pp. 10–24.

    Google Scholar 

  5. 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 

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

  7. A. S. Romanyuk, “Trigonometric widths of the classes B r p ??of functions of many variables in the space L q,” Ukr. Mat. Zh., 50, No. 8, 1089–1097 (1998).

    Google Scholar 

  8. Sun Yongsheng and Wang Heping, “Representation and approximation of multivariate periodic functions with bounded mixed moduli of smoothness,” Tr. Mat. Inst. RAN, 219, 356–377 (1997).

    Google Scholar 

  9. 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 

  10. É. S. Belinskii and É. M. Galeev, “On the least value of norms of mixed derivatives of trigonometric polynomials with given number of harmonics,” Vestn. Mosk. Univ., Ser. Mat. Mekh., No. 2, 3–7 (1991).

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

    Google Scholar 

  12. G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, Cambridge, (1934).

    Google Scholar 

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

    Google Scholar 

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Stasyuk, S.A. Trigonometric Widths of the Classes B Ω p of Periodic Functions of Many Variables. Ukrainian Mathematical Journal 54, 862–868 (2002). https://doi.org/10.1023/A:1021647800536

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