关于$\bbC^2$中的复（非解析）切比雪夫多项式
On Complex (non analytic) Chebyshev Polynomials in $\bbC^2$
摘要：
考虑了用复系数的低次多项式在$\bbC^2$中的单位球上找到标准单项式的最佳一致逼近问题。我们减少了问题的一维加权最小化问题的一个区间。在某种意义上，相应的极值多项式是经典正交雅可比多项式的一致对应。它们可以用梳状域上的特殊共形映射表示。在这些条件下，给出了原问题的最小偏差值和最佳逼近多项式的表示。此外，我们推导出最小偏差的渐近性。
英文摘要：
We consider the problem of finding a best uniform approximation to the standard monomial on the unit ball in $\bbC^2$ 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.
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