Đề tài "Bounds for polynomials with a unit discrete norm "

Let E be the set of N equidistant points in (−1, 1) and Pn (E) be the set of all polynomials P of degree ≤ n with max{|P (ζ)|, ζ ∈ E} ≤ 1. We prove that π Kn,N (x) = max |P (x)| ≤ C log , √ N P ∈Pn (E) arctan n r2 − x2 |x| ≤ r := 1 − n2 /N 2 where n