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arXiv · 2103.13349

Pointwise convergence of the non-linear Fourier transform

Alexei Poltoratski
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Abstract

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.

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Alexei Poltoratski. 2021-03-24. Pointwise convergence of the non-linear Fourier transform. https://arxiv.org/abs/2103.13349

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