Direct theorems of approximation theory on quasiconformal arcs

V. V. Andrievskii

Izvestiya. Mathematics , Tome 16 (1981) no. 2, pp. 221-238.

Résumé

This paper studies the polynomial approximation of functions that are continuous on an arbitrary finite quasiconformal arc. Bounds are obtained for the degree of approximation, including bounds depending on the position of the point at which the deviation of the approximating polynomial from the given function is studied, and also uniform bounds (independent of the point). The bounds of the first kind extend results of Dzyadyk, Lebedev and Shirokov, and Kolesnik to arbitrary quasiconformal arcs, which may, in particular, have no rectifiable subarcs. The bounds of the second kind are analogs of the results that Dzjadyk and Alibekov established for piecewise smooth arcs without cusps. Bibliography: 18 titles.

Bibliographie

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