Uniform convergence of the Bieberbach polynomials in closed smooth domains of bounded boundary rotation.

DOI10.1016/j.jat.2003.09.008zbMath1043.30023OpenAlexW2010187965MaRDI QIDQ1418951

Daniyal M. Israfilov

Publication date: 14 January 2004

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2003.09.008

zbMATH Keywords

rate of convergenceuniform convergenceBieberbach polynomialsconformal mappingbounded rotationsmooth boundaries

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25)

Related Items

An approximation of conformal mappings on smooth domains ⋮ Approximation properties of Julia polynomials ⋮ Simultaneous approximation of conformal mappings on smooth domains ⋮ Convergence of Bieberbach polynomials: Keldysh’s theorems and Mergelyan’s conjecture ⋮ Uniform convergence of the generalized Bieberbach polynomials in regions with simultaneously exterior and interior zero angles ⋮ Uniform convergence of some extremal polynomials in domain with corners on the boundary ⋮ Uniform convergence of the \(p\)-Bieberbach polynomials in domains with zero angles ⋮ Approximate properties of the p-Bieberbach polynomials in regions with simultaneously exterior and interior zero angles

Cites Work

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• On the boundary continuity of conformal maps
• Convergence of Bieberbach polynomials in domains with quasiconformal boundary
• On a polynomial lemma of Andrievskii
• On the convergence of the Bieberbach polynomials in regions with corners
• Polynomial approximation of conformal maps
• Polynomials orthogonal over a region and Bieberbach polynomials
• On conformal mapping of certain classes of Jordan domains
• ON THE CONVERGENCE OF BIEBERBACH POLYNOMIALS IN THE CASE OF A LIPSCHITZ DOMAIN
• Convergence of Bieberbach polynomials in domains with interior cusps
• Approximation by \(p\)-Faber polynomials in the weighted Smirnov class \(E^p(G,\omega)\) and the Bieberbach polynomials

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