Divergence of the Fourier series by generalized Haar systems at points of continuity of a function

Abstract

We obtain a connection between the Dirichlet kernels and partial Fourier sums by generalized Haar and Walsh (Price) systems. Based on this, we establish an interrelation between convergence of the Fourier series by generalized Haar and Walsh (Price) systems. For any unbounded sequence we construct a model of continuous function on a group (and even on a segment [0, 1]), whose Fourier series by generalized Haar system generated by this sequence, diverges at some point.