English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This chapter is a companion of a recent paper, entitled 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 twofold. First we try to explain methods and results, and give further straightforward corollaries. On the other hand, we also push forward the methods to obtain a better constant for the possible concentration (in the L 1 norm) of an idempotent on an arbitrary symmetric measurable set of positive measure. We prove a rather high level γ1 > 0. 96, which contradicts strongly the conjecture of Anderson et al. that there is no positive concentration in the L 1 norm. The same problem is considered on the group  \mathbbZ/q\mathbbZ\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.

Concentration of the Integral Norm of Idempotents