Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Widder's representation theorem for symmetric local Dirichlet spaces   In classical PDE theory, Widder's theorem gives a representation for
nonnegative solutions of the heat equation on $\mathbb{R}^n$. We show that an
analogous theorem holds for local weak solutions of the canonical "heat
equation" on a symmetric local Dirichlet space satisfying a local parabolic
Harnack inequality.

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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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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: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-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: hep-ex
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The categories of this paper are: hep-ph