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arXiv · 0903.3652

Asymptotics of the best polynomial approximation of $|x|^p$ and of the best Laurent polynomial approximation of $\sgn(x)$ on two symmetric intervals

F. Nazarov·F. Peherstorfer·A. Volberg·P. Yuditskii
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Abstract

We present a new method that allows us to get a direct proof of the classical Bernstein asymptotics for the error of the best uniform polynomial approximation of $|x|^p$ on two symmetric intervals. Note, that in addition, we get asymptotics for the polynomials themselves under a certain renormalization. Also, we solve a problem on asymptotics of the best approximation of $\sgn(x)$ on $[-1,-a]\cup[a,1]$ by Laurent polynomials.

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F. Nazarov, F. Peherstorfer, A. Volberg, P. Yuditskii. 2009-03-21. Asymptotics of the best polynomial approximation of $|x|^p$ and of the best Laurent polynomial approximation of $\sgn(x)$ on two symmetric intervals. https://arxiv.org/abs/0903.3652

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