Estimate of the remainder in the asymptotic solution of an extremal problem involving nonnegative trigonometric polynomials
type: Item
instance of: scholarly article
title: Estimate of the remainder in the asymptotic solution of an extremal problem involving nonnegative trigonometric polynomials
zbMATH Open document ID: 1362.42001
DOI: 10.1134/S0001434616070294
published in: Mathematical Notes
publication date: 2017-02-08T00:00:00Z
review text: Let \(K(\gamma)=\inf_\alpha\{-\min_x\sum_{k=1}^\infty\alpha_k\cos(kx)\}\), for real sequences \(\alpha=(\alpha_1;\dots)\) with either \(\alpha_k=0\) or \(\alpha_k\geq 1\) and \(\sum_{k=1}^\infty\alpha_k=\gamma\), and \(K^{\downarrow}(\gamma)\) is the \(K(\gamma)\) for decreasing sequences \(\alpha\). The given paper is one in a series of papers by the author, where he obtains estimates for these quantities. The \(K(\gamma)\) was introduced by \textit{A. M. Odlyzko} [J. Lond. Math. Soc., II. Ser. 26, 412--420 (1982; Zbl 0476.30005)].
Mathematics Subject Classification ID: 42A05
zbMATH DE Number: 6682163
zbMATH Keywords: extremal trigonometric polynomial
zbMATH Keywords: extremal problem
zbMATH Keywords: asymptotic estimate
author: A. S. Belov
MaRDI profile type: Publication
cites work: Minima of Cosine Sums and Maxima of Polynomials on the Unit Circle
cites work: Q3955834
cites work: Hardy's inequality and the \(L^ 1\) norm of exponential sums
full work available at URL: s0001434616070294
OpenAlex ID: W2516954510
description: scientific article; zbMATH DE number 6682163