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Mat. Sb., 2020, Volume 211, Number 1, Pages 125–174 (Mi msb9201)  

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.

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).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm9201

Full text: PDF file (980 kB)
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English version:
Sbornik: Mathematics, 2020, 211:1, 115–160

Bibliographic databases:

UDC: 512.75+511.687+512.547.4
MSC: 11S80, 43A70
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”, Mat. Sb., 211:1 (2020), 125–174; Sb. Math., 211:1 (2020), 115–160

Citation in format AMSBIB
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\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.
\yr 2020
\vol 211
\issue 1
\pages 125--174
\mathnet{http://mi.mathnet.ru/msb9201}
\crossref{https://doi.org/10.4213/sm9201}
\transl
\jour Sb. Math.
\yr 2020
\vol 211
\issue 1
\pages 115--160
\crossref{https://doi.org/10.1070/SM9201}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85083250305}


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  • https://doi.org/10.4213/sm9201
  • http://mi.mathnet.ru/eng/msb/v211/i1/p125

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. N. Parshin, “The Mellin Transform and the Plancherel Theorem for the Discrete Heisenberg Group”, Proc. Steklov Inst. Math., 307 (2019), 174–192  mathnet  crossref  crossref  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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