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Fast decreasing polynomials. (English) Zbl 0682.41014
Summary: Matching two-sided estimates are given for the minimal degree of polynomials P satisfying \(P(0)=1\) and \(| P(x)| \leq \exp (-\phi (| x|))\), \(x\in [-1,1]\), where \(\phi\) is an arbitrary, in [0,1], increasing function. Besides these fast decreasing polynomials we also consider bell-shaped polynomials and polynomials approximating well the signum function.

41A10 Approximation by polynomials
26C05 Real polynomials: analytic properties, etc.
41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)
Full Text: DOI
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