Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dixmier traces and residues on weak operator ideals   We develop the theory of modulated operators in general principal ideals of
compact operators. For Laplacian modulated operators we establish Connes' trace
formula in its local Euclidean model and a global version thereof. It expresses
Dixmier traces in terms of the vector-valued Wodzicki residue. We demonstrate
the applicability of our main results in the context of log-classical
pseudo-differential operators, studied by Lesch, and a class of operators
naturally appearing in noncommutative geometry.

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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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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: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc