Concentration of the integral norm of idempotents
| dc.creator | Bonami, Aline | |
| dc.creator | Révész, Szilárd Gy. | |
| dc.date | 2008-11-27 | |
| dc.date.accessioned | 2026-07-07T12:06:14Z | |
| dc.date.available | 2026-07-07T12:06:14Z | |
| dc.description | This is a companion paper of a recent one, entitled {\sl Integral concentration of idempotent trigonometric polynomials with gaps}. New results of the present work concern $L^1$ concentration, while the above mentioned paper deals with $L^p$-concentration. Our aim here is two-fold. At the first place we try to explain methods and results, and give further straightforward corollaries. On the other hand, we push forward the methods to obtain a better constant for the possible concentration (in $L^1$ norm) of an idempotent on an arbitrary symmetric measurable set of positive measure. We prove a rather high level $γ_1>0.96$, which contradicts strongly the conjecture of Anderson et al. that there is no positive concentration in $L^1$ norm. The same problem is considered on the group $\mathbb{Z}/q\mathbb{Z}$, with $q$ say a prime number. There, the property of absolute integral concentration of idempotent polynomials fails, which is in a way a positive answer to the conjecture mentioned above. Our proof uses recent results of B. Green and S. Konyagin on the Littlewood Problem. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/0811.4576 | |
| dc.identifier | http://arxiv.org/abs/0811.4576 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/208596 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42A05;42A16 | |
| dc.title | Concentration of the integral norm of idempotents | |
| dc.type | text |