Harmonic analysis on the rank-$2$ value group of a two-dimensional local field.
2020
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 the rank-$2$ 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.
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