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Complex Polynomials and Maximal Ranges: Background and Applications

  • Vladimir V. Andrievskii
  • Stephan Ruscheweyh
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 430)

Abstract

This survey is dedicated to the discussion of the various aspects of the notion of maximal polynomial ranges. These are the unions of ranges of polynomials restricted by a geometrical condition. The theory of maximal ranges in essentially constructive and permits in many cases the identification of extremal functions. It thereby leads to a unified approach to many old and new inequalities for polynomials. We also discuss the relation of this concept to the approximation of conformai maps in the unit disk by univalent polynomials.

Key words and phrases

Maximal ranges Complex polynomials Univalent polynomials Conformai mappings 

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Vladimir V. Andrievskii
    • 1
  • Stephan Ruscheweyh
    • 2
  1. 1.Institute for Applied Mathematics and Mechanics of the National Ukrainian Academy of SciencesDonetskUkraine
  2. 2.Mathematisches InstitutUniversität WürzburgWürzburgGermany

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