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arXiv · 2311.03511

Convergence from the discrete to the continuous non-linear Fourier transform

Ashley R. Zhang
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Abstract

In this note, we study the convergence from the discrete to the continuous non-linear Fourier transform. Relations between spectral problems and questions in complex function theory provide a new approach to the study of scattering problems and the non-linear Fourier transform \cite{Scatter}. In particular, the non-linear Fourier transform can be viewed from the perspective of spectral problems for differential operators. Results in \cite{MP, PZ} can be seen as results for the non-linear Fourier transform. These results are similar to some convergence problems for the discrete non-linear Fourier transform considered in \cite{T} and \cite{TT}.

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Ashley R. Zhang. 2023-11-06. Convergence from the discrete to the continuous non-linear Fourier transform. https://arxiv.org/abs/2311.03511

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