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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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