5 papers
Probabilistic Fourier extension and the Schrödinger equation
Lyudmila Korobenko, Eric T. Sawyer
We give applications of the probabilistic Fourier extension theorem for the paraboloid in d dimensions (see [Saw7] for the sphere, and the proof there holds for a smooth compact pi…
A smooth Alpert testing characterization of convolution type for the Fourier extension conjecture on paraboloids
Cristian Rios, Eric T. Sawyer
We prove a smooth Alpert testing characterization of convolution type for the Fourier extension conjecture on paraboloids, that further extends the characterizations in arXiv:2506.…
A single scale smooth Alpert trilinear characterization of the Fourier extension conjecture on the paraboloid in three dimensions
Cristian Rios, Eric T. Sawyer
We show that the Fourier extension conjecture on the paraboloid in three dimensions is equivalent to a local single scale smooth Alpert trilinear inequality, which is an improvemen…
Equivalence of linear and trilinear Kakeya conjectures in three dimensions
Cristian Rios, Eric T. Sawyer
We prove the equivalence of two Kakeya conjectures: 1.The Kakeya maximal operator conjecture 2.The disjoint trilinear dual form of the Kakeya maximal operator conjecture
Trilinear characterizations of the Fourier extension conjecture on the paraboloid in three dimensions
Cristian Rios, Eric Sawyer
We prove that a local trilinear extension inequality on the paraboloid in three dimensions is equivalent to the Fourier restriction conjecture, and then we prove a variant involvin…