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This article is cited in 1 scientific paper (total in 1 paper)
Harmonic analysis on the rank-$2$ value group of a two-dimensional local field
D. V. Osipovabc, A. N. Parshina a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b National Research University Higher School of Economics, Moscow, Russia
c National University of Science and Technology «MISiS», Moscow, Russia
Abstract:
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, Fourier transform, discrete Heisenberg groups.
Received: 27.11.2018 and 29.10.2019
Citation:
D. V. Osipov, A. N. Parshin, “Harmonic analysis on the rank-$2$ value group of a two-dimensional local field”, Sb. Math., 211:1 (2020), 115–160
Linking options:
https://www.mathnet.ru/eng/sm9201https://doi.org/10.1070/SM9201 https://www.mathnet.ru/eng/sm/v211/i1/p125
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Abstract page: | 785 | Russian version PDF: | 110 | English version PDF: | 19 | References: | 45 | First page: | 26 |
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