Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Inverse Spectral Problem for Jacobi-Type Pencils   In this paper we study the inverse spectral problem for Jacobi-type pencils.
By a Jacobi-type pencil we mean the following pencil $J_5 - \lambda J_3$, where
$J_3$ is a Jacobi matrix and $J_5$ is a semi-infinite real symmetric
five-diagonal matrix with positive numbers on the second subdiagonal. In the
case of a special perturbation of orthogonal polynomials on a finite interval
the corresponding spectral function takes an explicit form.

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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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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: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin