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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)
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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
Russian version:
Uspekhi Matematicheskikh Nauk, 2015, Volume 70, Issue 6(426), Pages 63–84
DOI: https://doi.org/10.4213/rm9687
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”, Uspekhi Mat. Nauk, 70:6(426) (2015), 63–84; Russian Math. Surveys, 70:6 (2015), 1031–1050
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/rm/v70/i6/p63
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:805
    Russian version PDF:261
    English version PDF:32
    References:71
    First page:81
     
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