Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher order $\Sc^2$-differentiability and application to Koplienko
  trace formula   Let $A$ be a selfadjoint operator in a separable Hilbert space, $K$ a
selfadjoint Hilbert-Schmidt operator, and $f\in C^n(\mathbb{R})$. We establish
that $\varphi(t)=f(A+tK)-f(A)$ is $n$-times continuously differentiable on
$\mathbb{R}$ in the Hilbert-Schmidt norm, provided either $A$ is bounded or the
derivatives $f^{(i)}$, $i=1,\ldots,n$, are bounded. As an application of the
second order $\Sc^2$-differentiability, we extend the Koplienko trace formula
from the Besov class $B_{\infty1}^2(\R)$ to functions $f$ for which the divided
difference $f^{[2]}$ admits a certain Hilbert space factorization.

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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph