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Remez-Type Inequalities in the Complex Plane

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Constructive Approximation Aims and scope

Abstract

We obtain a sharp upper bound on the modulus of a complex polynomial p(z) at any boundary point of a domain \(G\subset\mbox{\bf C}\) bounded by the Jordan curve without cusps. The area of the subset of G, where \(|p(z)|\le 1,\) is known.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA

    Vladimir V. Andrievskii

  2. Mathematisches Institut, Universitat Wurzburg, D-97074, Wurzburg, Germany

    Stephan Ruscheweyh

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  1. Vladimir V. Andrievskii
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  2. Stephan Ruscheweyh
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Correspondence to Vladimir V. Andrievskii or Stephan Ruscheweyh.

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Andrievskii, V., Ruscheweyh, S. Remez-Type Inequalities in the Complex Plane. Constr Approx 25, 221–237 (2007). https://doi.org/10.1007/s00365-006-0640-9

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  • DOI: https://doi.org/10.1007/s00365-006-0640-9

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