The Problem of Approximation in Mean on Arcs in the Complex Plane

J. I. Mamedkhanov

Matematičeskie zametki, Tome 99 (2016) no. 5, pp. 698-714

Résumé

Classical theorems on the approximation of curves in the complex domain are studied; in particular, direct and inverse theorems on the arcs $\Gamma$ in the complex plane in the metric of $L_p(\Gamma)$ are obtained. The results obtained are new in the case of a closed interval $[-1,1]$ as well.

Détail

Keywords: approximation of curves in the complex domain, Jackson–Bernstein theorem, Lipschitz condition, Newman problem, Jordan curve, Jackson–Dzyadyk polynomial, Minkowski inequality.

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