FROM INGHAM TO NAZAROV'S INEQUALITY: A SURVEY ON SOME TRIGONOMETRIC INEQUALITIES
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | JAMING, Philippe | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | SABA, Chadi | |
| dc.date.accessioned | 2024-04-04T02:32:20Z | |
| dc.date.available | 2024-04-04T02:32:20Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190375 | |
| dc.description.abstractEn | The aim of this paper is to give an overview of some inequalities about $L^p$-norms ($p= 1$ or $p= 2$) of harmonic (periodic) and non-harmonic trigonometric polynomials. Among the material covered, we mention Ingham's Inequality about 2 norms of non-harmonic trigonometric polynomials, the proof of the Littlewood conjecture by Mc Gehee, Pigno and Smith on the lower bound of the 1 norm of harmonic trigonometric polynomials as well as its counterpart in the non-harmonic case due to Nazarov. For the latter one, we give a quantitative estimate that completes our recent result with an estimate of 1-norms over small intervals. We also give some stronger lower bounds when the frequencies satisfy some more restrictive conditions (lacunary Fourier series, "multi-step arithmetic sequences"). Most proofs are close to existing ones and some open questions are mentioned at the end. | |
| dc.language.iso | en | |
| dc.subject.en | Ingham's Inequality | |
| dc.subject.en | Littlewood problem | |
| dc.subject.en | non-harmonic Fourier series | |
| dc.subject.en | lacunary series | |
| dc.title.en | FROM INGHAM TO NAZAROV'S INEQUALITY: A SURVEY ON SOME TRIGONOMETRIC INEQUALITIES | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Analyse classique [math.CA] | |
| dc.identifier.arxiv | 2311.17714 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-04314308 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04314308v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=JAMING,%20Philippe&SABA,%20Chadi&rft.genre=preprint |
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