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The best M-term trigonometric approximations of the classes of periodic multivariate functions with bounded generalized derivative in the space L q

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Abstract

The order estimates of the best M-term trigonometric approximations of functions \( {D}_{\beta}^{\psi } \) and the classes of (ψ , β)-differentiable periodic multivariate functions in the space L q , 2 ≤ q < ∞ are obtained. It is shown that, under certain conditions imposed on the parameter q; the best M-term trigonometric approximations \( {e}_M{\left({L}_{\beta, 1}^{\psi}\right)}_q \) have better order than the best orthogonal trigonometric approximations \( e\frac{1}{M}{\left({L}_{\beta, 1}^{\psi}\right)}_q \).

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Authors and Affiliations

  1. Institute of Mathematics of the NAS of Ukraine, Kiev, Ukraine

    Kateryna V. Shvai

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  1. Kateryna V. Shvai
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Correspondence to Kateryna V. Shvai.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 13, No. 3, pp. 361–375 July–September, 2016.

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Shvai, K.V. The best M-term trigonometric approximations of the classes of periodic multivariate functions with bounded generalized derivative in the space L q . J Math Sci 222, 750–761 (2017). https://doi.org/10.1007/s10958-017-3329-0

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  • DOI: https://doi.org/10.1007/s10958-017-3329-0

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