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Trigonometric Widths of the Classes L Ψ β,p of Functions of Many Variables

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Ukrainian Mathematical Journal Aims and scope

Abstract

We obtain order estimates for the trigonometric widths of the classes L Ψ β,p of periodic functions of many variables in the space L q for 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. A. I. Stepanets, Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).

    Google Scholar 

  3. A. S. Romanyuk, “Approximation of periodic functions of many variables in the metric of L q,” in: Approximation of Periodic Functions in the Metric of the Space L p [in Russian], Preprint No. 87.47, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1987), pp. 42–58.

    Google Scholar 

  4. 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).

  5. V. N. Temlyakov, “Approximation of functions with bounded mixed derivative,” Tr. Mat. Inst. Akad. Nauk SSSR, 178, 3–112 (1986).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  8. A. S. Romanyuk, “Estimates for the best approximations and widths of classes L ψβ , p of periodic functions of many variables,” in: Approximation of Classes of Functions of One and Many Variables in the Metrics of C and L p [in Russian], Preprint No. 88.14, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1988), pp. 29–59.

    Google Scholar 

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

    Google Scholar 

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

    N. M. Konsevych

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  1. N. M. Konsevych
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Konsevych, N.M. Trigonometric Widths of the Classes L Ψ β,p of Functions of Many Variables. Ukrainian Mathematical Journal 53, 1561–1567 (2001). https://doi.org/10.1023/A:1014331111819

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