Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The spectral form of Koopman representations of the group of measurable
  functions with values in the circle   We compute the spectral form of the Koopman representation induced by a
natural boolean action of $L^0(\lambda, {\mathbb T})$ identified earlier by the
authors. Our computation establishes the sharpness of the constraints on
spectral forms of Koopman representations of $L^0(\lambda, {\mathbb T})$
previously found by the second author.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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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: physics
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph