On a Theorem of Andrievskii and Ruscheweyh
نویسنده
چکیده
In a recent paper, V. V. Andrievskii and St. Ruscheweyh proved the existence of a universal real constant c > 0, such that for any conformal map f in the unit disk D and any n 2c, there exists a univalent polynomial pn in D of degree n with f(0) = pn(0) and f(nD) pn(D) f(D); where n := 1 ? c n : The numbers n are related to the quality of polynomial approximation of conformal maps. In this note, we show that 73 is an upper bound for the best possible c.
منابع مشابه
The maximal range problem for a bounded domain
Let Ω ⊂ C be a bounded domain such that 0 ∈ Ω . Denote by Pn, n ∈ N := {1, 2, . . .}, the set of all complex polynomials of degree at most n. Let Pn(Ω) := {p ∈ Pn : p(0) = 0, p(D) ⊂ Ω}, where D := {z : |z| < 1}. We relate the maximal polynomial range Ωn := ⋃ p∈Pn(Ω) p(D) to the geometry of Ω . Published by Elsevier Inc.
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