On some Leindler's theorem on application of the class NMCS

TL;DR

This paper extends Leindler's theorem by demonstrating strong approximation results for Fourier series using matrix means derived from the NMCS class, contributing to the understanding of convergence properties in harmonic analysis.

Contribution

It introduces new results linking Leindler's theorem to the class NMCS, expanding the scope of strong approximation techniques for Fourier series.

Findings

Established strong approximation results for Fourier series with NMCS sequences.

Connected Leindler's theorem to the class GM(5b) in Fourier analysis.

Enhanced understanding of matrix means in Fourier series convergence.

Abstract

We show the results in the class GM(5b) corresponding to the theorem of L. Leindler [A note on strong approximation of Fourier series, Analysis Mathematica, 29(2003), 195--199] on strong approximation by matrix means of Fourier series constructed by the sequences from the class NMCS.