On Complex (Non-Analytic) Chebyshev Polynomials in ℂ2

Ionela Moale, Peter Yuditskii

Research output: Contribution to journalArticlepeer-review


We consider the problem of finding a best uniform approximation to the standard monomial on the unit ball in ℂ2 by polynomials of lower degree with complex coefficients. We reduce the problem to a one-dimensional weighted minimization problem on an interval. In a sense, the corresponding extremal polynomials are uniform counterparts of the classical orthogonal Jacobi polynomials. They can be represented by means of special conformal mappings on the so-called comb-like domains. In these terms, the value of the minimal deviation and the representation for a polynomial of best approximation for the original problem are given. Furthermore, we derive asymptotics for the minimal deviation.

Original languageEnglish
Pages (from-to)13-24
Number of pages12
JournalComputational Methods and Function Theory
Issue number1
StatePublished - 2011
Externally publishedYes


  • Asymptotics
  • Conformal mapping
  • Minimal deviation
  • Polynomial approximation
  • Several variables
  • Uniform norm


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