Sets with interior extremal points for the Markoff inequality (Q5939941)

Let \(E\subset {\mathbb R}\) be a set consisting of several intervals. Then \(\|P'_n\|_E \leq M_n\|P_n\|_E\) holds for every polynomial \(P_n\) of degree at most \(n\) with some smallest constant \(M_n\), which is called \(n\)th Markov factor for~\(E\). The authors prove that there is a set \(E\) consisting of three intervals such that all extreme points for~\(M_5\) lie in the interior of~\(E\).