Concepts of generalized bounded variation and the theory of Fourier series

Abstract

The aim of this article is to unify a large part of present knowledge about the behaviour of Fourier series of functions of generalized bounded variation. The connections between various concepts are discussed, particular attention being payed to those due to Waterman and Chanturiya. Exploiting the existing interactions and utilizing the power of one or another approach to some typical questions of the Fourier theory, a number of previously unnoticed results are obtained in the course of this exposition.

Keywords

• Fourier series
• generalized bounded variation
• uniform and absolute convergences
• Gibb's phenomenon.