Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Pseudospectrum of Systems of Semiclassical Operators   The pseudospectra (or spectral instability) of non-selfadjoint operators is a
topic of current interest in applied mathematics. In fact, for non-selfadjoint
operators the resolvent could be very large outside the spectrum, making the
numerical computation of the complex eigenvalues very hard. This has
importance, for example, in quantum mechanics, random matrix theory and fluid
dynamics.
  The occurence of pseudospectra for non-selfadjoint semiclassical differential
operators is due to the existence of quasimodes, i.e., approximate local
solutions to the eigenvalue problem. For scalar operators, the quasimodes
appear since the bracket condition is not satisfied for topological reasons,
see the paper by Dencker, Sjostrand and Zworski in Comm. Pure Appl. Math. 57
(2004), 384-415.
  In this paper we shall investigate how these result can be generalized to
square systems of semiclassical differential operators of principal type. These
are the systems whose principal symbol vanishes of first order on its kernel.
We show that the resolvent blows up as in the scalar case, except in a nowhere
dense set of degenerate values. We also define quasi-symmetrizable systems and
systems of subelliptic type for which we prove estimates on the resolvent.

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The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th