A constrained optimization problem for the Fourier transform: Existence
Classical Analysis and ODEs
2019-08-28 v2
Abstract
Among functions majorized by indicator functions of sets with measure one, which functions have maximal Fourier transforms in the 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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Cite
@article{arxiv.1802.01743,
title = {A constrained optimization problem for the Fourier transform: Existence},
author = {Dominique Maldague},
journal= {arXiv preprint arXiv:1802.01743},
year = {2019}
}
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37 pages