Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bernstein functions of several semigroup generators on Banach spaces
  under bounded perturbations. II   The paper deals with multidimensional Bochner-Phillips functional calculus.
In the previous paper by the author bounded perturbations of Bernstein
functions of several commuting semigroup generators on Banach spaces where
considered, conditions for Lipschitzness and estimates for the norm of
commutators of such functions where proved. Also in the one-dimensional case
the Frechet differentiability of Bernstein functions of semigroup generators on
Banach spaces where proved and a generalization of Livschits-Kre\u{i}n trace
formula derived. The aim of the present paper is to prove the Frechet
differentiability of operator Bernstein functions and the Livschits-Kre\u{i}n
trace formula in the multidimensional setting.

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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: stat
8
The categories of this paper are: hep-ex