Harmonic analysis on the rank- value group of a two-dimensional local field

Abstract

In this work we construct a harmonic analysis on free Abelian groups of rank , namely: we construct and investigate spaces of functions and distributions, Fourier transforms and actions of discrete and extended discrete Heisenberg groups. In the case of the rank- value group of a two-dimensional local field with finite last residue field we connect this harmonic analysis with harmonic analysis on the two-dimensional local field, where the latter harmonic analysis was constructed in earlier works by the authors. Bibliography: 15 titles.