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Estimation of the Best Bilinear Approximations for the Classes of (ψ, Β)-Differentiable Periodic Multivariable Functions

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Ukrainian Mathematical Journal Aims and scope

Order estimates are established for the best bilinear approximations of 2d-variable functions \( f\left(x-y\right),x,y\in {\uppi}_d,{\uppi}_d=\prod {}_{j=1}^d\left[-\uppi, \uppi \right] \), formed by d-variable functions \( f(x)\in {L}_{\beta, p}^{\psi } \)

by the shifts of their argument x ∈ πd by all possible values of y ∈ πd in the space Lq1,q2(π2d). The results include various relations between the parameters p, q1, and q2.

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  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    K.V. Shvai

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  1. K.V. Shvai
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 4, pp. 564–573, April, 2018.

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Shvai, K. Estimation of the Best Bilinear Approximations for the Classes of (ψ, Β)-Differentiable Periodic Multivariable Functions. Ukr Math J 70, 649–660 (2018). https://doi.org/10.1007/s11253-018-1522-z

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  • DOI: https://doi.org/10.1007/s11253-018-1522-z

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