In this work we construct a harmonic analysis on free Abelian groups of rank ##IMG## [http://ej.iop.org/images/1064-5616/211/1/115/toc_MSB_211_1_115ieqn1.gif] {$2$} , 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- ##IMG## [http://ej.iop.org/images/1064-5616/211/1/115/toc_MSB_211_1_115ieqn1.gif] {$2$} 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.

中文翻译：

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等级上的谐波分析-## IMG ## [http://ej.iop.org/images/1064-5616/211/1/115/toc_MSB_211_1_115ieqn1.gif] {$ 2 $}二维局部值组领域

在这项工作中，我们对排名为## IMG ##的免费阿贝尔群进行谐波分析[http://ej.iop.org/images/1064-5616/211/1/115/toc_MSB_211_1_115ieqn1.gif] {$ 2 $} ，即：我们构造和研究函数和分布，傅立叶变换以及离散和扩展离散海森堡群的作用的空间。如果是排名-## IMG ## [http://ej.iop.org/images/1064-5616/211/1/115/toc_MSB_211_1_115ieqn1.gif] {$ 2 $}二维值组具有有限最后残差场的局部场，我们将此谐波分析与二维局部场的谐波分析联系起来，后者的谐波分析是作者在较早的工作中构建的。参考书目：15种。