An estimate of the constant term of a nonnegative trigonometric polynomial with integer coefficients
type: Item
instance of: scholarly article
title: An estimate of the constant term of a nonnegative trigonometric polynomial with integer coefficients
zbMATH Open document ID: 0871.42001
DOI: 10.1007/BF02308695
published in: Mathematical Notes
publication date: 1997-07-14T00:00:00Z
review text: A sequence \(\Lambda= \{\lambda_n\}^\infty_{n=1}\) of positive numbers is said to be admissible if \[ \sum^\infty_{n=1} {1\over \lambda_n} <\infty \quad \text{and} \quad \sum^\infty_{n=1} \sin\left({x \over\lambda_n} \right)\geq 0 \] for all \(x\geq 0\). If, moreover, \[ \sum^\infty_{n=1} \sin\left( {x\over\lambda_n} \right)>0 \] for all \(x>0\), then the sequence \(\Lambda\) is said to be strictly admissible. This definition was introduced by the first author. The aim of the present paper is to study admissible sequences and to use them to estimate the constant term of a nonnegative trigonometric polynomial with integer coefficients.
Mathematics Subject Classification ID: 42A05
Mathematics Subject Classification ID: 42A32
zbMATH DE Number: 1028548
zbMATH Keywords: admissible sequences
zbMATH Keywords: constant term
zbMATH Keywords: nonnegative trigonometric polynomial with integer coefficients
author: A. S. Belov
author: Sergei Konyagin
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf02308695
OpenAlex ID: W2051691123
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description: scientific article; zbMATH DE number 1028548