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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2411.04220 |
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| _version_ | 1866909772076285952 |
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| author | Sussman, Ethan |
| author_facet | Sussman, Ethan |
| contents | Recent work by Hintz--Vasy provides a partial asymptotic analysis of the low-energy limit of scattering for Schrödinger operators with a short-range potential. Using a slight refinement of Hintz's algorithm, we complete the asymptotic analysis by providing full asymptotic expansions in every possible asymptotic regime. Moreover, the analysis is done in any dimension $d\geq 3$, for any asymptotically conic manifold, and we keep track of partial multipole expansions. Applications include full asymptotic analyses of the Schrödinger, wave, and Klein--Gordon equations, one of these being described in a companion paper. Using previous work, only partial asymptotic analyses were possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04220 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complete asymptotic analysis of low energy scattering for Schrodinger operators with a short-range potential Sussman, Ethan Analysis of PDEs Primary 35C20. Secondary 58J50 Recent work by Hintz--Vasy provides a partial asymptotic analysis of the low-energy limit of scattering for Schrödinger operators with a short-range potential. Using a slight refinement of Hintz's algorithm, we complete the asymptotic analysis by providing full asymptotic expansions in every possible asymptotic regime. Moreover, the analysis is done in any dimension $d\geq 3$, for any asymptotically conic manifold, and we keep track of partial multipole expansions. Applications include full asymptotic analyses of the Schrödinger, wave, and Klein--Gordon equations, one of these being described in a companion paper. Using previous work, only partial asymptotic analyses were possible. |
| title | Complete asymptotic analysis of low energy scattering for Schrodinger operators with a short-range potential |
| topic | Analysis of PDEs Primary 35C20. Secondary 58J50 |
| url | https://arxiv.org/abs/2411.04220 |