Gaussians Rarely Extremize Adjoint Fourier Restriction Inequalities For\n Paraboloids

2010/12/06 by Michael Christ, Christ, Michael, René Quilodrán +1 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1012.1346

openalex publication_date 2010/12/06 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

It was proved independently by Foschi and Hundertmark, Zharnitsky that\nGaussians extremize the adjoint Fourier restriction inequality for L²\nfunctions on the paraboloid in the two lowest-dimesional cases. Here we prove\nthat Gaussians are critical points for the L^p to L^q adjoint Fourier\nrestriction inequalities if and only if p=2. Also, Gaussians are critial points\nfor the L² to L^r_t L^q_x Strichartz inequalities for all admissible pairs\n(r,q) in (1,infinity)².\n

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