Proof of the Fourier extension conjecture on the paraboloid in d>2 by decomposing smooth Alpert projections, applying a bilinear reduction, and bounding the resulting oscillatory integral with periodic amplitude via lattice averaging and stationary phase.
Zygmund, On Fourier coefficients and transforms of functions of two variables, Studia Mathematica 50 (1974), no
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Discusses two alternative proofs of Fefferman's Fourier extension theorem using decoupling and wavelet decompositions, with one method extended to higher dimensions.
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The Fourier extension conjecture for the paraboloid
Proof of the Fourier extension conjecture on the paraboloid in d>2 by decomposing smooth Alpert projections, applying a bilinear reduction, and bounding the resulting oscillatory integral with periodic amplitude via lattice averaging and stationary phase.
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A discussion of two new proofs of Fefferman's Fourier extension theorem in the plane
Discusses two alternative proofs of Fefferman's Fourier extension theorem using decoupling and wavelet decompositions, with one method extended to higher dimensions.