Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Riesz Decompositions for Schr\"odinger Operators on Graphs   We study superharmonic functions for Schr\"odinger operators on general
weighted graphs. Specifically, we prove two decompositions which both go under
the name Riesz decomposition in the literature. The first one decomposes a
superharmonic function into a harmonic and a potential part. The second one
decomposes a superharmonic function into a sum of superharmonic functions with
certain upper bounds given by prescribed superharmonic functions. As
application we show a Brelot type theorem.

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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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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: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg