Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harmonic functions on locally compact groups of polynomial growth   We extend a theorem by Kleiner, stating that on a group with polynomial
growth, the space of harmonic functions of polynomial of at most $k$ is finite
dimensional, to the settings of locally compact groups equipped with measures
with non-compact support. This has implications to the structure of the space
of polynomially growing harmonic functions.

6
The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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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: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph