Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the asymptotically simplicity of periodic eigenvalues and
  Titchmarsh's formula   We consider Sturm-Liouville equation $y^{\prime\prime}+(\lambda-q)y=0$ where
$q\in L^{1}[0,a]$. We obtain various conditions on the Fourier coefficients of
q such that the periodic eigenvalues having the form given by Titchmarsh are
asymptotically simple. Under these conditions, we give some asymptotic
estimates for the spectral gaps.

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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
9
The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int