Mathematics

On the Absolute Convergence of Fourier Series

T. Karchava

1997.7.1GEORGIAN MATHEMATICAL JOURNAL

DOI: 10.1515/gmj.1997.333

tlooto Summary

This paper deals with some problems of the absolute convergence of trigonometric Fourier series of a function from the class M, the class of all continuous 2π-periodic functions f for which there exists a partitioning of the segment [0, 2π] by the points.

Abstract

The necessary and sufficient conditions of the absolute convergence of a trigonometric Fourier series are established for continuous 2π-periodic functions which in [0, 2π] have a finite number of intervals of convexity, and whose nth Fourier coefficients are O(ω(l/n; f)/n), where ω(δ f) is the continuity modulus of the function f.

Citation format

KARCHAVA, T. On the absolute convergence of fourier series. GEORGIAN MATHEMATICAL JOURNAL, 1997, 4: 333–340.