Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral flow inside essential spectrum V: on absorbing points of
  coupling resonances   Let $H_0$ and $V$ be self-adjoint operators, such that $V$ admits a
factorisation $V = F^*JF$ with bounded self-adjoint $J$ and
$|H_0|^{1/2}$-compact $F.$ Coupling resonance functions, $r_j(z),$ of the pair
$H_0$ and $V$ can be defined as $r_j(z) = - \sigma_j(z) ^{-1},$ where
$\sigma_j(z)$ are eigenvalues of the compact-operator valued holomorphic
function $F(H_0-z)^{-1} F^*J.$ Taken together, the functions $r_j(z)$ form an
infinite-valued holomorphic function on the resolvent set of~$H_0.$ These
functions contain a lot of information about the pair $H_0, V$ (this is
well-known in the case of rank one $V$). A point $z_0$ of the resolvent set we
call \emph{absorbing} if some $r_j(z)$ goes to $\infty$ as $z \to z_0$ along
some half-interval.
  In this note I present some partial results concerning absorbing points of
coupling resonances.

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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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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: funct-an