How to concentrate idempotents
type: Item
instance of: scholarly article
title: How to concentrate idempotents
zbMATH Open document ID: 1202.42006
author: J. M. Ash
published in: Real Analysis Exchange
publication date: 2010-09-02T00:00:00Z
review text: An idempotent is defined as a finite sum \[ f(x)= \exp(2\pi N_1x)+\cdots\exp(2\pi N_mx), \] where \(N_1,\dots, N_m\) are integers. It is said that there holds \(L^p\)-concentration, if there exists a \(c_p> 0\) such that for each interval \(I\subset\mathbb{T}= [-1/2,1/2]\) and each \(\varepsilon> 0\) there exists an idempotent \(f\) such that \[ \Biggl(\int_I |f(x)|^p dx\Biggr)/ \Biggl(\int_{\mathbb{T}} |f(x)|^p dx\Biggr)> c_p- \varepsilon. \] The paper is a survey of results concerning existence of \(L^p\)-concentration for \(p> 0\).
reviewed by: Julian Musielak
Mathematics Subject Classification ID: 42A05
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 5778782
zbMATH Keywords: trigonometric polynomials
zbMATH Keywords: idempotent
zbMATH Keywords: \(L^p\)-concentration
MaRDI profile type: Publication
OpenAlex ID: W1569610633
DOI: 10.14321/REALANALEXCH.35.1.0001
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description: scientific article; zbMATH DE number 5778782