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Convergence of Bieberbach polynomials in domains with interior cusps

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Abstract

We extend the results on the uniform convergence of Bieberbach polynomials for 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 thecritical 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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Authors and Affiliations

  1. Institute of Biomathematics and Biometry, GSF-National Research Center for Environment and Health, D-85764, Neuherberg, Germany

    V. V. Andrievskii

  2. Department of Mathematics 401 Mathematical Sciences, Oklahoma State University, 74078-1058, Stillwater, OK, USA

    I. E. Pritsker

Authors
  1. V. V. Andrievskii
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  2. I. E. Pritsker
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Corresponding author

Correspondence to V. V. Andrievskii.

Additional information

Research of both authors was supported in part by the National Science Foundation grant DMS-9707359. Research of the second author was also supported in part by the National Science Foundation grant DMS-9970659.

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Andrievskii, V.V., Pritsker, I.E. Convergence of Bieberbach polynomials in domains with interior cusps. J. Anal. Math. 82, 315–332 (2000). https://doi.org/10.1007/BF02791232

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  • DOI: https://doi.org/10.1007/BF02791232

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