Akademik Veri Yönetim Sistemi
Journal of Approximation Theory, cilt.137, sa.2, ss.143-165, 2005 (SCI-Expanded, Scopus)
Let G ⊂ ℂ be a domain with a Jordan boundary ∂G, consisting of l smooth curves Γj, such that {zj} := Γj-1 ∩ Γj ≠ ∅, j = 1,..., l, where Γ0 := Γl. Denote by αjπ, 0 < αj ≤ 2, the angles at zj's between the curves Γj-1 and Γj, exterior with respect to G. Let Φ be a conformal mapping of the exterior ℂ\Ḡ of Ḡ = G ∪ ∂G onto the exterior of the unit disk, normed by Φ′(∞) > 0. We assume that there is a neighborhood U of Ḡ, such that 0 < c(G) ≤ φ(z) Φ′(z) ≤ C(G), z ∈ U\Ḡ, where φ(z) := ∏j=1l z-zj 1-1/alpha;j, z ∈ ℂ, z ≠ zj if αj ≤ 1. Set ∥g∥G := sup { g(z) : z ∈ G}. Then we prove Theorem. Let r ∈ ℕ and 0 ≤ β ≤ r. If a function f is analytic in G and ∥f(r) φβ∥G < + ∞, then for each n ≥ lr there is an algebraic polynomial Pn of degree < n, such that ∥(f - Pn)φβ-r∥G ≤ c(r, G)/nr∥ f(r)φβ ∥G. © 2005 Elsevier Inc. All rights reserved.