Geodesic
On a new discretization of complex analysis
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 6, pp. 1031-1050

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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. 
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     author = {I. A. Dynnikov},
     title = {On a new discretization of complex analysis},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     volume = {70},
     number = {6},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2015_70_6_a1/}
}
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I. A. Dynnikov. On a new discretization of complex analysis. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 6, pp. 1031-1050. http://geodesic.mathdoc.fr/item/RM_2015_70_6_a1/