Convergence from the discrete to the continuous non-linear Fourier transform
Classical Analysis and ODEs
2024-08-16 v2 Complex Variables
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}.
Cite
@article{arxiv.2311.03511,
title = {Convergence from the discrete to the continuous non-linear Fourier transform},
author = {Ashley R. Zhang},
journal= {arXiv preprint arXiv:2311.03511},
year = {2024}
}