@article{13d7bbbd34ef49819907398e02a5fed4,
title = "Asymptotics of the best polynomial approximation of |χ|p and of the best laurent polynomial approximation of sgn(x) on two symmetric intervals",
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 |χ|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]∪[a,1] by Laurent polynomials.",
keywords = "Bernstein constant, Chebyshev theorem, Conformal mapping, Hilbert transform",
author = "F. Nazarov and F. Peherstorfer and A. Volberg and P. Yuditskii",
year = "2009",
month = feb,
doi = "10.1007/s00365-008-9007-1",
language = "אנגלית",
volume = "29",
pages = "23--39",
journal = "Constructive Approximation",
issn = "0176-4276",
publisher = "Springer New York",
number = "1",
}