A lower bound for the minimum deviation of the Chebyshev polynomial on a compact real set

On Complex (non analytic) Chebyshev Polynomials in $\bbC^2$

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…

Hsiang三次式作为球面上的切比雪夫多项式：等振荡与幂等求积

Hsiang cubics as spherical Chebyshev polynomials: equioscillation and idempotent quadrature

本文将Hsiang三次式与球面上的切比雪夫多项式关联，研究其等振荡性质、平稳性，证明Cartan等参三次式在特定维度下是最小偏差问题的全局极小元，还给出了相关求积恒等式与球面设计的结果。