Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pointwise convergence of the non-linear Fourier transform   We prove pointwise convergence for the scattering data of a Dirac system of
differential equations. Equivalently, we prove an analog of Carleson's theorem
on almost everywhere convergence of Fourier series for a version of the
non-linear Fourier transform. Our proofs are based on the study of resonances
of Dirac systems using families of meromorphic inner functions, generated by a
Ricatti equation corresponding to the system.

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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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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: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph