A problem of Totik on fast decreasing polynomials
The authors give a solution of the following problem on fast decreasing polynomials, posed some years ago by V. Totik: For given \(\beta>2\), determine the largest positive constant \(c\) such that there exists a sequence of polynomials \(p_n\in\Pi_n\) and a constant \(C\) satisfying \(p_n (0) =1\) and \(| p_n(x) |\leq C \exp (-cn | x|^\beta)\) for \(x\in [-1,1]\). The solution, i.e., the exact bound for the constant \(c\), is given implicitly using the solution of a certain integral equation, too complicated to be presented here.
scientific article; zbMATH DE number 1129641