On the uniform convergence of special sine integrals
type: Item
instance of: scholarly article
title: On the uniform convergence of special sine integrals
zbMATH Open document ID: 1250.42021
published in: Acta Mathematica Hungarica
publication date: 2011-12-20T00:00:00Z
review text: The title more or less reflects the subject of the paper: certain conditions are obtained that ensure the uniform convergence of the sine Fourier integrals. There are two main problems with this paper: novelty of the obtained results and introduced definitions and references. In fact, these problems are closely related: if the references were not incomplete and sometimes misleading, many of the results would not be published (at least, in the present form) because they were earlier obtained in the paper by \textit{M. Dyachenko, E. Liflyand} and \textit{S. Tikhonov} [J. Math. Anal. Appl. 372, 328--338 (2010; Zbl 1201.42003)]. In addition, the author claims that he generalizes his own results on trigonometric series from [Acta Math. Hungar. 128, 369--380 (2010; Zbl 1240.42015)] but in fact the paper by \textit{M. Dyachenko} and \textit{S. Tikhonov} [Stud. Math. 193, 285--306 (2009; Zbl 1169.42001)] should be mentioned as a real prototype. Not less important are the used classes of functions. As for the preceding analogs for sequences, they should be attributed to S. Tikhonov; the best reference here is the recent survey paper, both on sequences and functions, by \textit{E. Liflyand} and \textit{S. Tikhonov}, [Math. Nachr. 284, 1083--1098 (2011; Zbl 1223.26017)].
reviewed by: Elijah Liflyand
Mathematics Subject Classification ID: 42A32
Mathematics Subject Classification ID: 42A38
zbMATH DE Number: 5990914
zbMATH Keywords: sine integral
zbMATH Keywords: uniform convergence
zbMATH Keywords: supremum bounded variation sequence
zbMATH Keywords: supremum bounded variation function
zbMATH Keywords: mean value bounded variation sequence
zbMATH Keywords: mean value bounded variation function
author: Péter Kórus
MaRDI profile type: Publication
full work available at URL: s10474-010-0063-1
OpenAlex ID: W1987232288
cites work: Remarks on the uniform and \(L^1\)-convergence of trigonometric series
cites work: On the uniform convergence of sine integrals
cites work: Ultimate generalization to monotonicity for uniform convergence of trigonometric series
DOI: 10.1007/S10474-010-0063-1
description: scientific article; zbMATH DE number 5990914