Geodesic
Harmonic analysis on the rank-$2$ value group of a~two-dimensional local field
Sbornik. Mathematics, Tome 211 (2020) no. 1, pp. 115-160

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In this work we construct a harmonic analysis on free Abelian groups of rank $2$, 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-$2$ 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. Bibliography: 15 titles.
Keywords: two-dimensional local field, value group, harmonic analysis, discrete Heisenberg groups.
Mots-clés : Fourier transform 
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D. V. Osipov; A. N. Parshin. Harmonic analysis on the rank-$2$ value group of a~two-dimensional local field. Sbornik. Mathematics, Tome 211 (2020) no. 1, pp. 115-160. http://geodesic.mathdoc.fr/item/SM_2020_211_1_a3/