2019
Том 71
№ 8

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Best approximation and best unilateral approximation of the kernel of a biharmonic equation and optimal renewal of the values of operators

Shabozov M. Sh.

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Abstract

For the classB p ρ , 0 ≤ ρ < 1, 1≤p ≤ ∞, of 2π-periodic functions of the form f(t)=u(ρ,t), whereu (ρ,t) is a biharmonic function in the unit disk, we obtain the exact values of the best approximation and best unilateral approximation of the kernel Kρ(t) of the convolution f= Kρ *g, ∥g∥ρ≤l, with respect to the metric of L1. We also consider the problem of renewal of the values of the convolution operator by using the information about the values of the boundary functions.

English version (Springer): Ukrainian Mathematical Journal 47 (1995), no. 11, pp 1769-1778.

Citation Example: Shabozov M. Sh. Best approximation and best unilateral approximation of the kernel of a biharmonic equation and optimal renewal of the values of operators // Ukr. Mat. Zh. - 1995. - 47, № 11. - pp. 1549–1557.

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