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A problem of Totik on fast decreasing polynomials. (English) Zbl 0894.41008
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.
Reviewer: G.Walz (Mannheim)

MSC:
41A10 Approximation by polynomials
31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions
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