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Гармонический анализ на группе нормирования ранга 2 двумерного локального поля

Математический сборник. 2020. Т. 211. № 1. С. 125-174.
Осипов Д. В., Паршин А. Н.

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