Inverse Spectral Analysis of Singular Radial AKNS Operators
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915883391123456 |
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| author | Gobin, Damien Grébert, Benoît Helffer, Bernard Nicoleau, François |
| author_facet | Gobin, Damien Grébert, Benoît Helffer, Bernard Nicoleau, François |
| contents | We study an inverse spectral problem for singular AKNS operators based on
spectral data associated with two distinct values of the effective angular momentum
parameter $κ\,$.
Our main focus is the local inverse problem near the zero potential.
For the pairs $(κ_1,κ_2)=(0,1)$, $(1,2)$ and $(0,3)\,$, we establish local
uniqueness.
For $(0,2)\,$, we prove that the Fréchet differential of the spectral map
at the origin is injective, while the question whether its range is closed
remains open. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21961 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inverse Spectral Analysis of Singular Radial AKNS Operators Gobin, Damien Grébert, Benoît Helffer, Bernard Nicoleau, François Analysis of PDEs Mathematical Physics Spectral Theory We study an inverse spectral problem for singular AKNS operators based on spectral data associated with two distinct values of the effective angular momentum parameter $κ\,$. Our main focus is the local inverse problem near the zero potential. For the pairs $(κ_1,κ_2)=(0,1)$, $(1,2)$ and $(0,3)\,$, we establish local uniqueness. For $(0,2)\,$, we prove that the Fréchet differential of the spectral map at the origin is injective, while the question whether its range is closed remains open. |
| title | Inverse Spectral Analysis of Singular Radial AKNS Operators |
| topic | Analysis of PDEs Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2603.21961 |