Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simplicity and Finiteness of Discrete Spectrum of the Benjamin-Ono
  Scattering Operator   A spectral analysis is done on the $L$ operator of the Lax pair for the
Benjamin-Ono equation. Simplicity and finiteness of the discrete spectrum are
established as are needed for the Fokas and Ablowitz inverse scattering
transform scheme. A crucial step in the simplicity proof is the discovery of a
new identity connecting the $L^2$ norm of the eigenvector to its inner product
with the scattering potential. The proof for finiteness is an extension of the
ideas involved in the Birman-Schwinger bound for Schr\"odinger operators.

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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: q-fin