Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotics of the best polynomial approximation of $|x|^p$ and of the
  best Laurent polynomial approximation of $\sgn(x)$ on two symmetric intervals   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.

30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess