Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representation and Approximation of Positivity Preservers   We consider a closed set S in R^n and a linear operator \Phi on the
polynomial algebra R[X_1,...,X_n] that preserves nonnegative polynomials, in
the following sense: if f\geq 0 on S, then \Phi(f)\geq 0 on S as well. We show
that each such operator is given by integration with respect to a measure
taking nonnegative functions as its values. This can be seen as a
generalization of Haviland's Theorem, which concerns linear functionals on
polynomial algebras. For compact sets S we use the result to show that any
nonnegativity preserving operator is a pointwise limit of very simple
nonnegativity preservers with finite dimensional range.

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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat