On the Behavior of Algebraic Polynomial in Unbounded Regions with Piecewise Dini-Smooth Boundary

ABDULLAYEV F., Özkartepe P.

Ukrainian Mathematical Journal, vol.66, no.5, pp.645-665, 2014 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 66 Issue: 5
  • Publication Date: 2014
  • Doi Number: 10.1007/s11253-014-0962-3
  • Journal Name: Ukrainian Mathematical Journal
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.645-665
  • Uşak University Affiliated: No

Abstract

Let G ⊂ ℂ be a finite region bounded by a Jordan curve L := ∂G, let (formula presented)Ω(formula presented), let Δ := {w : |w| > 1}, and let w = Φ(z) be the univalent conformal mapping of Ω onto Δ normalized by Φ (∞) = ∞, Φ′(∞) > 0. Also let h(z) be a weight function and let Ap(h,G), p > 0 denote a class of functions f analytic in G and satisfying the condition(formula presented)where σ is a two-dimensional Lebesgue measure. Moreover, let Pn (z) be an arbitrary algebraic polynomial of degree at most n ∈ ℕ. The well-known Bernstein–Walsh lemma states that(formula presented) In this present work we continue the investigation of estimation (*) in which the norm (formula presented), for Jacobi-type weight function in regions with piecewise Dini-smooth boundary.