Convergence from the discrete to the continuous non-linear Fourier transform
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911988774338560 |
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| author | Zhang, Ashley R. |
| author_facet | Zhang, Ashley R. |
| contents | 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}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03511 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Convergence from the discrete to the continuous non-linear Fourier transform Zhang, Ashley R. Classical Analysis and ODEs Complex Variables 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}. |
| title | Convergence from the discrete to the continuous non-linear Fourier transform |
| topic | Classical Analysis and ODEs Complex Variables |
| url | https://arxiv.org/abs/2311.03511 |