Tauberian theorems with remainder for summation methods of the Gel'fand and Cesaro type

descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 1989 English Publisher:Springer Science and Business Media LLCJournal:Ukrainian Mathematical Journal, volume 41, pages 785-789 (issn: 0041-5995, eissn: 1573-9376,

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Authors: Mikhalin, G. A.;

doi: 10.1007/bf01060693

Tauberian theorems with remainder for summation methods of the Gel'fand and Cesaro type

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Abstract

Tauberian theorems on sequences from a linear locally convex space F are proved for Hölder and Cesàro methods. By special choice of F some earlier results of G. H. Hardy, R. Schmidt, N. A. Davydov and G. Kangro can be obtained from these theorems. Choosing the space of all continuous \(2\pi\)-periodic functions for F the author gives a result for uniform convergence of Fourier series.

Keywords

Tauberian theorems, Cesàro methods, Hölder method, uniform convergence of Fourier series

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