Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic upper bounds for the entropy of orthogonal polynomials in the
  Szeg\H{o} class   We give an asymptotic upper bound as $n\to\infty$ for the entropy integral
$$E_n(w)= -\int p_n^2(x)\log (p_n^2(x))w(x)dx,$$ where $p_n$ is the $n$th
degree orthonormal polynomial with respect to a weight $w(x)$ on $[-1,1]$ which
belongs to the Szeg\H{o} class. We also study two functionals closely related
to the entropy integral. First, their asymptotic behavior is completely
described for weights $w$ in the Bernstein class. Then, as for the entropy, we
obtain asymptotic upper bounds for these two functionals when $w(x)$ belongs to
the Szeg\H{o} class. In each case, we give conditions for these upper bounds to
be attained.

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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an