Sparse Fourier restriction for the cone
In Fourier restriction theory, weighted inequalities allow us to probe the shape of level sets. In this thesis, we describe a new weighted Fourier extension estimate for the cone and its connection with the Mizohata–Takeuchi conjecture. The main result Theorem 3.1 builds on techniques from geometry...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2024
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| Online Access: | https://hdl.handle.net/1721.1/155321 |
| _version_ | 1826200379108360192 |
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| author | Ortiz, Alexander |
| author2 | Guth, Lawrence |
| author_facet | Guth, Lawrence Ortiz, Alexander |
| author_sort | Ortiz, Alexander |
| collection | MIT |
| description | In Fourier restriction theory, weighted inequalities allow us to probe the shape of level sets. In this thesis, we describe a new weighted Fourier extension estimate for the cone and its connection with the Mizohata–Takeuchi conjecture. The main result Theorem 3.1 builds on techniques from geometry originally explored by Tom Wolff in this context. The proof uses circular maximal function estimates first proved by Wolff and later generalized by Pramanik–Yang–Zahl in their work on restricted projections as a black box. |
| first_indexed | 2024-09-23T11:35:29Z |
| format | Thesis |
| id | mit-1721.1/155321 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T11:35:29Z |
| publishDate | 2024 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1553212024-06-28T03:37:31Z Sparse Fourier restriction for the cone Ortiz, Alexander Guth, Lawrence Massachusetts Institute of Technology. Department of Mathematics In Fourier restriction theory, weighted inequalities allow us to probe the shape of level sets. In this thesis, we describe a new weighted Fourier extension estimate for the cone and its connection with the Mizohata–Takeuchi conjecture. The main result Theorem 3.1 builds on techniques from geometry originally explored by Tom Wolff in this context. The proof uses circular maximal function estimates first proved by Wolff and later generalized by Pramanik–Yang–Zahl in their work on restricted projections as a black box. Ph.D. 2024-06-27T19:44:49Z 2024-06-27T19:44:49Z 2024-05 2024-05-15T16:20:47.448Z Thesis https://hdl.handle.net/1721.1/155321 Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) Copyright retained by author(s) https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Ortiz, Alexander Sparse Fourier restriction for the cone |
| title | Sparse Fourier restriction for the cone |
| title_full | Sparse Fourier restriction for the cone |
| title_fullStr | Sparse Fourier restriction for the cone |
| title_full_unstemmed | Sparse Fourier restriction for the cone |
| title_short | Sparse Fourier restriction for the cone |
| title_sort | sparse fourier restriction for the cone |
| url | https://hdl.handle.net/1721.1/155321 |
| work_keys_str_mv | AT ortizalexander sparsefourierrestrictionforthecone |