Fourier decoupling for convex sequences
We study the decoupling theory for functions on R with Fourier transform sup- ported in a neighborhood of a convex sequence [formula], where [formula] and 𝑔 : [0, 1] → R is a 𝐶² function satisfying 𝑔′(𝑥) > 0, 𝑔′′(𝑥) > 0 for every 𝑥 ∈ [0, 1]. We utilize the wave packet structure of functions wi...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Published: |
Massachusetts Institute of Technology
2023
|
| Online Access: | https://hdl.handle.net/1721.1/151597 |
| _version_ | 1811078450289573888 |
|---|---|
| author | Fu, Yuqiu |
| author2 | Guth, Lawrence |
| author_facet | Guth, Lawrence Fu, Yuqiu |
| author_sort | Fu, Yuqiu |
| collection | MIT |
| description | We study the decoupling theory for functions on R with Fourier transform sup- ported in a neighborhood of a convex sequence [formula], where [formula] and 𝑔 : [0, 1] → R is a 𝐶² function satisfying 𝑔′(𝑥) > 0, 𝑔′′(𝑥) > 0 for every 𝑥 ∈ [0, 1]. We utilize the wave packet structure of functions with frequency support in a neigh- borhood of an arithmetic progression. |
| first_indexed | 2024-09-23T11:00:04Z |
| format | Thesis |
| id | mit-1721.1/151597 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T11:00:04Z |
| publishDate | 2023 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1515972023-08-01T03:59:53Z Fourier decoupling for convex sequences Fu, Yuqiu Guth, Lawrence Massachusetts Institute of Technology. Department of Mathematics We study the decoupling theory for functions on R with Fourier transform sup- ported in a neighborhood of a convex sequence [formula], where [formula] and 𝑔 : [0, 1] → R is a 𝐶² function satisfying 𝑔′(𝑥) > 0, 𝑔′′(𝑥) > 0 for every 𝑥 ∈ [0, 1]. We utilize the wave packet structure of functions with frequency support in a neigh- borhood of an arithmetic progression. Ph.D. 2023-07-31T19:51:24Z 2023-07-31T19:51:24Z 2023-06 2023-05-24T14:46:45.010Z Thesis https://hdl.handle.net/1721.1/151597 In Copyright - Educational Use Permitted Copyright retained by author(s) https://rightsstatements.org/page/InC-EDU/1.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Fu, Yuqiu Fourier decoupling for convex sequences |
| title | Fourier decoupling for convex sequences |
| title_full | Fourier decoupling for convex sequences |
| title_fullStr | Fourier decoupling for convex sequences |
| title_full_unstemmed | Fourier decoupling for convex sequences |
| title_short | Fourier decoupling for convex sequences |
| title_sort | fourier decoupling for convex sequences |
| url | https://hdl.handle.net/1721.1/151597 |
| work_keys_str_mv | AT fuyuqiu fourierdecouplingforconvexsequences |