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Showing 1 to 2 of 2 for “"Restriction theory"”.
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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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Linear and bilinear restriction estimates for the Fourier transform
This thesis is concerned with the restriction theory of the Fourier transform. We prove two restriction estimates for the Fourier transform. The first is a bilinear estimate for the light cone when the exponents are on a critical line. This extends results proven by Wolff, Tao and Lee-Vargas. The …