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arXiv · 1012.1346

Gaussians Rarely Extremize Adjoint Fourier Restriction Inequalities For Paraboloids

Michael Christ·René Quilodrán
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Abstract

It was proved independently by Foschi and Hundertmark, Zharnitsky that Gaussians extremize the adjoint Fourier restriction inequality for L^2 functions on the paraboloid in the two lowest-dimesional cases. Here we prove that Gaussians are critical points for the L^p to L^q adjoint Fourier restriction inequalities if and only if p=2. Also, Gaussians are critial points for the L^2 to L^r_t L^q_x Strichartz inequalities for all admissible pairs (r,q) in (1,infinity)^2.

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Michael Christ, René Quilodrán. 2010-12-06. Gaussians Rarely Extremize Adjoint Fourier Restriction Inequalities For Paraboloids. https://arxiv.org/abs/1012.1346

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