Harmonic analysis on the rank-$2$ value group of a two-dimensional local field
Number Theory
2020-03-23 v3 Algebraic Geometry
Representation Theory
Abstract
In this work we construct harmonic analysis on free Abelian groups of rank , 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- 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.
Keywords
Cite
@article{arxiv.1911.09718,
title = {Harmonic analysis on the rank-$2$ value group of a two-dimensional local field},
author = {D. V. Osipov and A. N. Parshin},
journal= {arXiv preprint arXiv:1911.09718},
year = {2020}
}
Comments
48 pages; the title is slightly changed; to appear in Sbornik: Mathematics 211:1 (2020)