Generalized Vilenkin Groups

Generalized Vilenkin groups are introduced and studied. To such a group, there corresponds an arbitrary finite Abelian group instead of a cyclic group in the case of classical Vilenkin groups. The foundations of harmonic analysis and methods for constructing wavelets on generalized Vilenkin groups are developed. It is proved that the additive group of any local field of positive characteristic is a generalized Vilenkin group.