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 +1

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 sym…