Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral deformation for two-body dispersive systems with e.g. the
  Yukawa potential   We find an explicit closed formula for the $k$'th iterated commutator
$\mathrm{ad}_A^k(H_V(\xi))$ of arbitrary order $k\ge1$ between a Hamiltonian
$H_V(\xi)=M_{\omega_\xi}+S_{\check V}$ and a conjugate operator
$A=\frac{\mathfrak{i}}{2}(v_\xi\cdot\nabla+\nabla\cdot v_\xi)$, where
$M_{\omega_\xi}$ is the operator of multiplication with the real analytic
function $\omega_\xi$ which depends real analytically on the parameter $\xi$,
and the operator $S_{\check V}$ is the operator of convolution with the
(sufficiently nice) function $\check V$, and $v_\xi$ is some vector field
determined by $\omega_\xi$. Under certain assumptions, which are satisfied for
the Yukawa potential, we then prove estimates of the form
$\lVert\mathrm{ad}_A^k(H_V(\xi))(H_0(\xi)+\mathfrak{i})^{-1}\rVert\le
C_\xi^kk!$ where $C_\xi$ is some constant which depends continuously on $\xi$.
The Hamiltonian is the fixed total momentum fiber Hamiltonian of an abstract
two-body dispersive system and the work is inspired by a recent result
[Engelmann-M{\o}ller-Rasmussen, 2015] which, under conditions including
estimates of the mentioned type, opens up for spectral deformation and analytic
perturbation theory of embedded eigenvalues of finite multiplicity.

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The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
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The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom