On absolutely divergent Fourier series

A method of constructing series mentioned in the title in many dimen-\break sions is discussed. This method yields series representing functions of smoothness slightly ligher than for those in the class $C^{(d/2)}(\mathbb T^d)$ and is based on an analog of the de Leeuw–Katznelson–Kahane theorem for the classes $C^{(l)}(\mathbb T^d)$.