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Sbornik: Mathematics, 2020, Volume 211, Issue 1, Pages 115–160
DOI: https://doi.org/10.1070/SM9201 (Mi sm9201) 		 
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
English version PDF (795 kB) Citations (1)
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DOI: https://doi.org/10.1070/SM9201
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.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.641.31.0001
The research of D. V. Osipov was partially supported by the Laboratory of Mirror Symmetry, National Research University Higher School of Economics (Russian Federation government grant, ag. no. 14.641.31.0001).
Received: 27.11.2018 and 29.10.2019
Russian version:
Matematicheskii Sbornik, 2020, Volume 211, Number 1, Pages 125–174
DOI: https://doi.org/10.4213/sm9201
Bibliographic databases:
Document Type: Article
UDC: 512.75+511.687+512.547.4
MSC: 11S80, 43A70
Language: English
Original paper language: Russian
Citation: D. V. Osipov, A. N. Parshin, “Harmonic analysis on the rank-$2$ value group of a two-dimensional local field”, Mat. Sb., 211:1 (2020), 125–174; Sb. Math., 211:1 (2020), 115–160
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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    References:44
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