$\ell^1$ mapping properties, smoothness and decay for $SU(2)$-valued nonlinear Fourier transform
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917306063388672 |
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| author | Mnatsakanyan, Gevorg |
| author_facet | Mnatsakanyan, Gevorg |
| contents | We prove an analog of Baxter's theorem for $SU(2)$-valued nonlinear Fourier transform (NLFT). That is, we prove that under certain natural conditions on the NLFT data, the potential is in $\ell^1$ if and only if the linear Fourier coefficients of the NLFT data are in $\ell^1$. Furthermore, we prove some smoothness-decay estimates for the NLFT motivated by similar estimates for the linear Fourier transform. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02021 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $\ell^1$ mapping properties, smoothness and decay for $SU(2)$-valued nonlinear Fourier transform Mnatsakanyan, Gevorg Classical Analysis and ODEs 42C99, 81P68, 34L25, 47B35 We prove an analog of Baxter's theorem for $SU(2)$-valued nonlinear Fourier transform (NLFT). That is, we prove that under certain natural conditions on the NLFT data, the potential is in $\ell^1$ if and only if the linear Fourier coefficients of the NLFT data are in $\ell^1$. Furthermore, we prove some smoothness-decay estimates for the NLFT motivated by similar estimates for the linear Fourier transform. |
| title | $\ell^1$ mapping properties, smoothness and decay for $SU(2)$-valued nonlinear Fourier transform |
| topic | Classical Analysis and ODEs 42C99, 81P68, 34L25, 47B35 |
| url | https://arxiv.org/abs/2603.02021 |