On the Fourier transform of the symmetric decreasing rearrangements
| hal.structure.identifier | Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | JAMING, Philippe | |
| dc.date.accessioned | 2024-04-04T02:46:59Z | |
| dc.date.available | 2024-04-04T02:46:59Z | |
| dc.date.created | 2008 | |
| dc.date.issued | 2011 | |
| dc.identifier.issn | 0373-0956 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191601 | |
| dc.description.abstractEn | Inspired by work of Montgomery on Fourier series and Donoho-Strak in signal processing, we investigate two families of rearrangement inequalities for the Fourier transform. More precisely, we show that the $L^2$ behavior of a Fourier transform of a function over a small set is controlled by the $L^2$ behavior of the Fourier transform of its symmetric decreasing rearrangement. In the $L^1$ case, the same is true if we further assume that the function has a support of finite measure. As a byproduct, we also give a simple proof and an extension of a result of Lieb about the smoothness of a rearrangement. Finally, a straightforward application to solutions of the free Shrödinger equation is given. | |
| dc.description.sponsorship | Analyse Harmonique et Problèmes Inverses - ANR-07-BLAN-0247 | |
| dc.language.iso | en | |
| dc.publisher | Association des Annales de l'Institut Fourier | |
| dc.subject.en | Fourier transform | |
| dc.subject.en | rearrangement inequalities | |
| dc.subject.en | Bessel functions | |
| dc.title.en | On the Fourier transform of the symmetric decreasing rearrangements | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Analyse classique [math.CA] | |
| dc.identifier.arxiv | 0809.0604 | |
| bordeaux.journal | Annales de l'Institut Fourier | |
| bordeaux.page | 53-77 | |
| bordeaux.volume | 61 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00316922 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00316922v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Annales%20de%20l'Institut%20Fourier&rft.date=2011&rft.volume=61&rft.spage=53-77&rft.epage=53-77&rft.eissn=0373-0956&rft.issn=0373-0956&rft.au=JAMING,%20Philippe&rft.genre=article |
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