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Linear and Kolmogorov Widths of the Classes \( {B}_{p,\uptheta}^{\Omega} \) of Periodic Functions of One and Several Variables

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Abstract. Some estimates exact in order for linear widths of the classes \( {B}_{p,\uptheta}^{\Omega} \) of periodic multivariable functions in the space Lq with certain relations between the parameters p, q; and 𝜃 are obtained. In the univariate case, the estimates exact in order for Kolmogorov and linear widths of the classes \( {B}_{\infty, \uptheta}^{\omega } \) in the space Lq, 1 ≤ q ≤ ∞; are established.

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Authors and Affiliations

  1. Lesya Ukrainka East-European National University, Luts’k, Ukraine

    Mykhailo V. Hembars’kyi & Svitlana B. Hembars’ka

Authors
  1. Mykhailo V. Hembars’kyi
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  2. Svitlana B. Hembars’ka
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Correspondence to Mykhailo V. Hembars’kyi or Svitlana B. Hembars’ka.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 17, No. 2, pp. 171–187 April–June, 2020

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Hembars’kyi, M.V., Hembars’ka, S.B. Linear and Kolmogorov Widths of the Classes \( {B}_{p,\uptheta}^{\Omega} \) of Periodic Functions of One and Several Variables. J Math Sci 249, 720–732 (2020). https://doi.org/10.1007/s10958-020-04968-x

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  • DOI: https://doi.org/10.1007/s10958-020-04968-x

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