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

Abstract

In this work we construct harmonic analysis on free Abelian groups of rank 2 , namely: we construct and investigate spaces of functions and distributions, Fourier transforms, actions of discrete and extended discrete Heisenberg groups. In case of rank 2 value group of a 2 -dimensional local field with the finite last residue field we connect this harmonic analysis with harmonic analysis on the 2 -dimensional local field, where the last harmonic analysis was constructed earlier in works of authors.