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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let f be a sum of exponentials of the form exp(2 pi i N x), where the N aredistinct integers. We call f an idempotent trigonometric polynomial (becausethe convolution of f with itself is f) or, simply, an idempotent. We show thatfor every p > 1, and every set E of the torus T = R/Z with |E| > 0, there areidempotents concentrated on E in the Lp sense. More precisely, for each p > 1,there is an explicitly calculated constant Cp > 0 so that for each E with |E| >0 and epsilon > 0 one can find an idempotent f such that the pth root of theratio of the integral over E of the pth power of |f| to the integral over T ofthe pth power of |f| is greater than Cp - epsilon. This is in fact a lowerbound result and, though not optimal, it is close to the best that our methodgives. We also give both heuristic and computational evidence for the stillopen problem of whether the Lp concentration phenomenon fails to occur when p =1.

Exponential sums with coefficients 0 or 1 and concentrated L^{p} norms