Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Dirichlet-to-Neumann Maps and Some Applications to Modified Fredholm
  Determinants   We consider Dirichlet-to-Neumann maps associated with (not necessarily
self-adjoint) Schrodinger operators in $L^2(\Omega; d^n x)$, $n=2,3$, where
$\Omega$ is an open set with a compact, nonempty boundary satisfying certain
regularity conditions. As an application we describe a reduction of a certain
ratio of modified Fredholm perturbation determinants associated with operators
in $L^2(\Omega; d^n x)$ to modified Fredholm perturbation determinants
associated with operators in $L^2(\partial\Omega; d^{n-1}\sigma)$, $n=2,3$.
This leads to a two- and three-dimensional extension of a variant of a
celebrated formula due to Jost and Pais, which reduces the Fredholm
perturbation determinant associated with a Schrodinger operator on the
half-line $(0,\infty)$ to a simple Wronski determinant of appropriate
distributional solutions of the underlying Schrodinger equation.

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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas