Convergence of Bieberbach polynomials in domains with interior cusps

Details Convergence of Bieberbach polynomials in domains with interior cusps Convergence of Bieberbach polynomials in domains with interior cusps

2000-01-24

arxiv.org/abs/math/0001122v1

Mathematics

Complex Variables

18 pages, AMS-LaTeX, to appear in J. d'Analyse Math

Scientific paper

We extend the results on the uniform convergence of Bieberbach polynomials to domains with certain interior zero angles (outward pointing cusps), and show that they play a special role in the problem. Namely, we construct a Keldysh-type example on the divergence of Bieberbach polynomials at an outward pointing cusp and discuss the critical order of tangency at this interior zero angle, separating the convergent behavior of Bieberbach polynomials from the divergent one for sufficiently thin cusps.

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