A method for estimating the \(L_1\) norm of an exponential sum based on arithmetic properties of the spectrum
type: Item
instance of: scholarly article
zbMATH Open document ID: 1007.42002
author: S. V. Bochkarev
publication date: 2003-03-07T00:00:00Z
Mathematics Subject Classification ID: 42A05
Mathematics Subject Classification ID: 42A16
Mathematics Subject Classification ID: 42A55
zbMATH DE Number: 1729318
zbMATH Keywords: \(L_p\) norms
zbMATH Keywords: trigonometric sums
zbMATH Keywords: distribution
zbMATH Keywords: spectrum points
zbMATH Keywords: dyadic blocks
MaRDI profile type: Publication
title: A method for estimating the \(L_1\) norm of an exponential sum based on arithmetic properties of the spectrum
review text: In his earlier papers, the author proved an estimate for the \(L_1\)-norms of trigonometric sums. That estimate depends on the distribution of the spectrum points over dyadic blocks and is sharp for both lacunary and nonlacunary spectra. In the used terms no improvement is possible. Hence in the paper under review not only distribution of the spectrum points over dyadic blocks is studied but also the arithmetic properties of the spectrum inside each dyadic block. The new lower estimate obtained is given in terms of the ratios of the \(L_p,\) \(p\geq 2,\) and \(L_2\) norms of dyadic blocks.NEWLINENEWLINEFor the entire collection see [Zbl 0981.00017].
reviewed by: Elijah Liflyand
description: scientific article; zbMATH DE number 1729318