Explicit formula for the fundamental class of functions ( Z, Z,Φ ) , introduced by J. Jorgenson and S. Lang, is given a new form valid for a more general fudge factor Φ. This is done for a larger class of test functions of generalized bounded variation.
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.
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