Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Order estimations of the best approximations and approximations of the
  Fourier sums on the classes of infinitely differentiable functions   We obtained order estimations for the best uniform approximations by
trigonometric polynomials and approximations by Fourier sums of classes of
$2\pi$-periodic continuous functions, which $(\psi,\beta)$-derivatives
$f_{\beta}^{\psi}$ belong to unit balls of spaces $L_{p}, 1\leq p<\infty$ in
case at consequences $\psi(k)$ decrease to nought faster than any power
function. We also established the analogical estimations in $L_{s}$-metric,
$1<s\leq\infty$, for classes of the summable $(\psi,\beta)$-differentiable
functions, such that $\parallel f_{\beta}^{\psi}\parallel_{1}\leq1$.

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The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph