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
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.
two-dimensional local field, value group, harmonic analysis, Fourier transform, discrete Heisenberg groups.
|Ministry of Education and Science of the Russian Federation
|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).
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Sbornik: Mathematics, 2020, 211:1, 115–160
MSC: 11S80, 43A70
Received: 27.11.2018 and 29.10.2019
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
\by D.~V.~Osipov, A.~N.~Parshin
\paper Harmonic analysis on the rank-$2$ value group of a~two-dimensional local field
\jour Mat. Sb.
\jour Sb. Math.
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This publication is cited in the following articles:
A. N. Parshin, “The Mellin Transform and the Plancherel Theorem for the Discrete Heisenberg Group”, Proc. Steklov Inst. Math., 307 (2019), 174–192
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