In this paper, supose Γ be a boundary of a Jordan domain D and Γ satisfied Альпер condition, the order that rational type interpolating operators at Fejer's points of f(z)∈C(Γ) converge to f(z) in the se...In this paper, supose Γ be a boundary of a Jordan domain D and Γ satisfied Альпер condition, the order that rational type interpolating operators at Fejer's points of f(z)∈C(Γ) converge to f(z) in the sense of uniformly convergence is obtained.展开更多
Let G C C be a simply connected domain whose boundary L ：= G is a Jordan curve and 0 ∈ G. Let w = φ（z） be the conformal mapping of G onto the disk B（0, r0） ：= {w ： ｜w｜ 〈 r0）, satisfying φ0（0） = 0, φ＇...Let G C C be a simply connected domain whose boundary L ：= G is a Jordan curve and 0 ∈ G. Let w = φ（z） be the conformal mapping of G onto the disk B（0, r0） ：= {w ： ｜w｜ 〈 r0）, satisfying φ0（0） = 0, φ＇t（0） = 1. We consider the following extremal problem for p 〉 0：∫∫G｜φ＇（z）-P＇n（z）｜Pdσz→min in the class of all polynomials Pn（z） of degree not exceeding n with Pn（0） = 0, P＇n （0）=- 1. The solution to this extremal problem is called the p-Bieberbach polynomial of degree n for the pair （G, 0）. We study the uniform convergence of the p-Bieberbach polynomials Bn,p（z） to the φ（z） on G^- with interior and exterior zero angles determined depending on the properties of boundary arcs and the degree of their ＂touch＂.展开更多
文摘In this paper, supose Γ be a boundary of a Jordan domain D and Γ satisfied Альпер condition, the order that rational type interpolating operators at Fejer's points of f(z)∈C(Γ) converge to f(z) in the sense of uniformly convergence is obtained.
文摘Let G C C be a simply connected domain whose boundary L ：= G is a Jordan curve and 0 ∈ G. Let w = φ（z） be the conformal mapping of G onto the disk B（0, r0） ：= {w ： ｜w｜ 〈 r0）, satisfying φ0（0） = 0, φ＇t（0） = 1. We consider the following extremal problem for p 〉 0：∫∫G｜φ＇（z）-P＇n（z）｜Pdσz→min in the class of all polynomials Pn（z） of degree not exceeding n with Pn（0） = 0, P＇n （0）=- 1. The solution to this extremal problem is called the p-Bieberbach polynomial of degree n for the pair （G, 0）. We study the uniform convergence of the p-Bieberbach polynomials Bn,p（z） to the φ（z） on G^- with interior and exterior zero angles determined depending on the properties of boundary arcs and the degree of their ＂touch＂.
