Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Best polynomial approximation on the unit ball   Let $E_n(f)_\mu$ be the error of best approximation by polynomials of degree
at most $n$ in the space $L^2(\varpi_\mu, \mathbb{B}^d)$, where $\mathbb{B}^d$
is the unit ball in $\mathbb{R}^d$ and $\varpi_\mu(x) = (1-\|x\|^2)^\mu$ for
$\mu > -1$. Our main result shows that, for $s \in \mathbb{N}$, $$ E_n(f)_\mu
\le c n^{-2s}[E_{n-2s}(\Delta^s f)_{\mu+2s} + E_{n}(\Delta_0^s f)_{\mu}], $$
where $\Delta$ and $\Delta_0$ are the Laplace and Laplace-Beltrami operators,
respectively. We also derive a bound when the right hand side contains odd
order derivatives.

37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas