{"title":"Approximation by a special de la Vallée Poussin type matrix transform mean of Vilenkin–Fourier series","authors":"I. Blahota, D. Nagy","doi":"10.1007/s10476-024-00049-2","DOIUrl":null,"url":null,"abstract":"<div><p>We consider the norm convergence for a special matrix-based de la Vallée Poussin-like mean of Fourier series with respect to the Vilenkin system. \nWe estimate the difference between the named mean above and the corresponding function in norm, and the upper estimation is given by the modulus of \ncontinuity of the function. We also give theorems with respect to norm and almost everywhere convergences.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"50 3","pages":"939 - 957"},"PeriodicalIF":0.6000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis Mathematica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10476-024-00049-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the norm convergence for a special matrix-based de la Vallée Poussin-like mean of Fourier series with respect to the Vilenkin system.
We estimate the difference between the named mean above and the corresponding function in norm, and the upper estimation is given by the modulus of
continuity of the function. We also give theorems with respect to norm and almost everywhere convergences.
期刊介绍：
Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx).
The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx).
The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.
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