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...
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| Formato: | Tesis |
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Massachusetts Institute of Technology
2023
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| Acceso en línea: | https://hdl.handle.net/1721.1/151597 |
| Sumario: | 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. |
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