Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Total positivity of a Cauchy kernel   We study the total positivity of the kernel $1/(x^2 + 2 \cos(\pi\a)xy +y^2).$
The case of infinite order is characterized by an application of Schoenberg's
theorem. We then give necessary conditions for the cases of any given finite
order with the help of Chebyshev polynomials of the second kind. Sufficient
conditions for the finite order cases are also obtained, thanks to Propp's
formula for the Izergin-Korepin determinant. As a by-product, we give a partial
answer to a question of Karlin on positive stable semi-groups.

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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex