Extremal polynomials on the \(n\)-grid (Q2689106)

In this article, limits of sequences of so-called extremal polynomials are studied. These extremal polynomials are defined on a net of equally spaced points on the unit interval \([-1,1]\), and they maximize the uniform norm of polynomials among all polynomials that have a bound of one on the net; they are also required to be of a certain maximal degree, defined by a multiple of the number of points. The particular limits that are studied are \(\log\|p^*_n\|_\infty/n\) as \(n\to\infty\).