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Uspekhi Mat. Nauk, 2015, Volume 70, Issue 6(426), Pages 63–84 (Mi umn9687)  

This article is cited in 2 scientific papers (total in 2 papers)

On a new discretization of complex analysis

I. A. Dynnikov

Steklov Mathematical Institute of Russian Academy of Sciences

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.


DOI: https://doi.org/10.4213/rm9687

Full text: PDF file (648 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2015, 70:6, 1031–1050

Bibliographic databases:

UDC: 517.962.22+517.547.9
MSC: Primary 39A12; Secondary 37J35
Received: 18.09.2015

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. I. A. Dynnikov, “Bounded discrete holomorphic functions on the hyperbolic plane”, Proc. Steklov Inst. Math., 302 (2018), 186–197  mathnet  crossref  crossref  isi  elib
  • Успехи математических наук Russian Mathematical Surveys
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