Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Norm convergence of multiple ergodic averages on amenable groups   We apply Walsh's method for proving norm convergence of multiple ergodic
averages to arbitrary amenable groups. We obtain convergence in the uniform
Ces\`aro sense for their polynomial actions and for ``triangular'' averages
associated to commuting homomorphic actions. The latter generalizes a result
due to Bergelson, McCutcheon, and Zhang in the case of two actions.

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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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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: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc