Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orthonormal bases of polynomials in one complex variable   Let a sequence $(P_n)$ of polynomials in one complex variable satisfy a
recurre ce relation with length growing slowlier than linearly. It is shown
that $(P_n) $ is an orthonormal basis in $L^2_{\mu}$ for some measure $\mu$ on
$\C$, if and o ly if the recurrence is a $3-$term relation with special
coefficients. The supp rt of $\mu$ lies on a straight line. This result is
achieved by the analysis of a formally normal irreducible Hessenberg operator
with only finitely many nonzero entries in every row. It generalizes the
classical Favard's Theorem and the Representation Theorem.

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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an