Extremal problems of Chebyshev type
Extremal problems of Chebyshev type
Let $a \in \mathbb {C} \setminus [-1,1]$ be given. We consider the problem of finding $\sup |p(a)|$ among all polynomials $p$ with complex coefficients of degree less than or equal to $n$ with $\max _{-1\leq x \leq 1}|p(x)| \leq 1$. We derive an asymptotic expression for the extremal polynomial and …