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Russian Mathematical Surveys, 2015, Volume 70, Issue 6, Pages 1031–1050
DOI: https://doi.org/10.1070/RM2015v070n06ABEH004973 (Mi rm9687) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On a new discretization of complex analysis

I. A. Dynnikov

Steklov Mathematical Institute of Russian Academy of Sciences
English version PDF (592 kB) Citations (3) Russian version article
References:
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DOI: https://doi.org/10.1070/RM2015v070n06ABEH004973
Abstract: This paper develops an approach to discretization of complex analysis proposed by S. P. Novikov and the author in 2003. Under this approach discrete analytic functions are real-valued. It is shown that a large class of such functions on a lattice admits a canonical multiplication by the imaginary unit. Arbitrary lattices are considered for a triangular discretization and rhombic lattices for a quadrangular discretization.
Bibliography: 24 titles.
Keywords: discrete analytic functions, discrete holomorphic functions, discretization of complex analysis.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.
Received: 18.09.2015
Bibliographic databases:
Document Type: Article
UDC: 517.962.22+517.547.9
MSC: Primary 39A12; Secondary 37J35
Language: English
Original paper language: Russian
Citation: I. A. Dynnikov, “On a new discretization of complex analysis”, Russian Math. Surveys, 70:6 (2015), 1031–1050
Citation in format AMSBIB
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\by I.~A.~Dynnikov
\paper On a new discretization of complex analysis
\jour Russian Math. Surveys
\yr 2015
\vol 70
\issue 6
\pages 1031--1050
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\crossref{https://doi.org/10.1070/RM2015v070n06ABEH004973}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3462715}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84962791889}
Linking options:
  • https://www.mathnet.ru/eng/rm9687
  • https://doi.org/10.1070/RM2015v070n06ABEH004973
  • https://www.mathnet.ru/eng/rm/v70/i6/p63
    • This publication is cited in the following 3 articles:
    1. Yuri Dabaghian, “Grid cells, border cells, and discrete complex analysis”, Front. Comput. Neurosci., 17 (2023)  crossref
    2. I. A. Dynnikov, “Bounded discrete holomorphic functions on the hyperbolic plane”, Proc. Steklov Inst. Math., 302 (2018), 186–197  mathnet  crossref  crossref  mathscinet  isi  elib
    3. D. A. Gorodkov, “A minimal triangulation of the quaternionic projective plane”, Russian Math. Surveys, 71:6 (2016), 1140–1142  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Statistics & downloads:
    Abstract page:869
    Russian version PDF:278
    English version PDF:47
    References:83
    First page:81
     
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