Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trace Formula For Two Variables   A natural generalization of Krein's theorem to a pair of commuting tuples
$\left(H_1^0,H_2^0\right)$ and $\left(H_1,H_2\right)$ of bounded self-adjoint
operators in a separable Hilbert space $\mathcal{H}$ with $H_j-H_j^0 = V_j\in
\mathcal{B}_2(\mathcal{H})$(set of all Hilbert-Schmidt operators on
$\mathcal{H}$) for $j=1,2,$ leads to a Stokes-like formula under trace. A major
ingredient in the proof is the finite-dimensional approximation result for
commuting self-adjoint n-tuples of operators, a generalization of Weyl-von
Neumann-Berg's theorem.

16
The categories of this paper are: stat
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The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc