Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral estimates for degenerate critical levels   We establish spectral estimates at a critical energy level for $h$-pseudors .
Via a trace formula, we compute the contribution of isolated (non-extremum)
critical points under a condition of "real principal type". The main result
holds for all dimensions, for a singularity of any finite order and can be
invariantly expressed in term of the geometry of the singularity. When the
singularities are not integrable on the energy surface the results are
significative since the order w.r.t. $h$ of the spectral distributions are
bigger than in the regular setting.

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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio