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020 ▼a 9781085780421
035 ▼a (MiAaPQ)AAI13860790
040 ▼a MiAaPQ ▼c MiAaPQ ▼d 247004
0820 ▼a 510
1001 ▼a Maldague, Dominique.
24510 ▼a A Constrained Optimization Problem for the Fourier Transform.
260 ▼a [S.l.]: ▼b University of California, Berkeley., ▼c 2019.
260 1 ▼a Ann Arbor: ▼b ProQuest Dissertations & Theses, ▼c 2019.
300 ▼a 89 p.
500 ▼a Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
500 ▼a Advisor: Christ, Michael.
5021 ▼a Thesis (Ph.D.)--University of California, Berkeley, 2019.
506 ▼a This item must not be sold to any third party vendors.
506 ▼a This item must not be added to any third party search indexes.
520 ▼a Among functions f majorized by indicator functions of sets E of measure 1, which functions have maximal Fourier transform in Lp? We investigate the existence of maximizers, using a concentration compactness approach and ingredients from additive combinatorics to establish properties of maximizing sequences. For exponents q sufficiently close to even integers, we exploit variational techniques and combinatorial results to identify all maximizers. This follows from establishing a sharper version of an associated inequality: if the input f, where |f| is less than or equal to the indicator function of a measure 1 set E, has a certain structure, then the Fourier transform of f in Lq is at least a certain quantitative distance from being optimal.
590 ▼a School code: 0028.
650 4 ▼a Mathematics.
690 ▼a 0405
71020 ▼a University of California, Berkeley. ▼b Mathematics.
7730 ▼t Dissertations Abstracts International ▼g 81-04B.
773 ▼t Dissertation Abstract International
790 ▼a 0028
791 ▼a Ph.D.
792 ▼a 2019
793 ▼a English
85640 ▼u http://www.riss.kr/pdu/ddodLink.do?id=T15490921 ▼n KERIS ▼z 이 자료의 원문은 한국교육학술정보원에서 제공합니다.
980 ▼a 202002 ▼f 2020
990 ▼a ***1816162
991 ▼a E-BOOK