2022/09/08 by Giuseppe Negro, Negro, Giuseppe, Diogo Oliveira e Silva +3
Mathematics · #42B10 #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2209.03916
openalex publication_date 2022/09/08 · openalex created_date 2022/09/11 · openalex updated_date 2026/07/28
In the past decade, much effort has gone into understanding maximizers for Fourier restriction and extension inequalities. Nearly all of the cases in which maximizers for inequalities involving the restriction or extension operator have been successfully identified can be seen as partial answers to the question in the title. In this survey, we focus on recent developments in sharp restriction theory relevant to this question. We present results in the algebraic case for spherical and hyperbolic extension inequalities. We also discuss the use of the Penrose transform leading to some negative answers in the case of the cone.