A constrained optimization problem for the Fourier transform: Existence

2018/02/06 by Maldague, Dominique
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.01743

Abstract

Among functions majorized by indicator functions of sets with measure one, which functions have maximal Fourier transforms in the L^q norm? We partially prove the existence of such functions using techniques from additive combinatorics to establish a conditional precompactness for maximizing sequences.

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