Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Essential spectrum of elliptic systems of pseudo-differential operators
  on $L^2(\mathbb{R}^N)\oplus L^2(\mathbb{R}^N)$   Inspired by a result of Wong (Commun. Partial Differ. Equ. 13(10):1209-1221,
1988), we establish an analytic description of the essential spectrum of
non-self-adjoint mixed-order systems of pseudo-differential operators on
$L^2(\mathbb{R}^N) \oplus L^2(\mathbb{R}^N)$ that are uniformly
Douglis-Nirenberg elliptic with positive-order diagonal entries. We apply our
result to a problem arising in the dynamics of falling liquid films.

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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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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: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat