Determination of the jump of a function of generalized bounded variation from the derivatives of the partial sums of its Fourier series

Abstract

It is established that the formulas determining the jump of a periodic function from the derivatives of the partial sums of its Fourier series and valid for functions of harmonic bounded variation (the HBV class) possibly will not hold for functions of Φ-bounded variation (in the sense of Schramm) if this class is wider than the HBV class.