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

2023/11/06 by Ashley R. Zhang, Zhang, Ashley R.
Mathematics · #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2311.03511

openalex publication_date 2023/11/06 · openalex created_date 2023/11/09 · openalex updated_date 2026/07/28

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 \citeScatter. In particular, the non-linear Fourier transform can be viewed from the perspective of spectral problems for differential operators. Results in \citeMP, 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 \citeT and \citeTT.

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