2010/02/10 by Ionela Moale, I. Moale, Moale, I. +3
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Matrix Theory and Algorithms #math.CA #math.CV
paper · pdf · doi:10.48550/arxiv.1002.2060
arxiv created 2010/02/10 · openalex publication_date 2010/02/10 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of finding a best uniform approximation to the standard monomial on the unit ball in \bbC2 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.