The Walsh transform of wavelet type systems: divergence almost everywhere

Abstract

The main result of the paper is the following: for the Walsh transform of a wavelet type system on [0, l], there is an integrable function whose Fourier expansion with respect to the transformed system is divergent almost everywhere on [0, l]. This is an extension of the result by K. S. Kazarian and A. S. Sargsian [9] for the bounded Ciesielski system, i.e. the Walsh transform of the Franklin system.