منابع مشابه
Discrete Analytic Functions: An Exposition
Harmonic and analytic functions have natural discrete analogues. Harmonic functions can be defined on every graph, while analytic functions (or, more precisely, holomorphic forms) can be defined on graphs embedded in orientable surfaces. Many important properties of the “true” harmonic and analytic functions can be carried over to the discrete setting.
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In [7] Pillay described the model-theoretic significance of a result in complex analytic geometry due to Campana [1] and Fujiki [2]. These notes are an exposition of the “jet space” constructions that underly the Campana/Fujiki theorem. In particular, we discuss infinitesimal neighbourhoods as well as the sheaves of principal parts, jets, and differential operators. The material is drawn largel...
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for every point (x, y) E Z, X Z, . If Z, x Z, is identified with the lattice (h(m + in); m, 1z integers} embedded in the complex plane, then condition (1.1) is seen to be an “analyticity” condition: On each unit square of the lattice, the difference quotients along the two diagonals are the same. The above definition of analyticity was introduced by Ferrand [I] and many properties of such funct...
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Lf(m,n)=f(m,n)+if(m+1,n)+i~f(m+1,n+1)+i3f(m,n+ 1) =o. (1.1) The concept of a discrete analytic function was introduced by Ferrand [l] and many properties of discrete analytic functions were obtained by D&in [2]. A convolution product for discrete analytic functions was defined by DufEn and Duris [3] and an operational calculus was developed by Hayabara [4] and further extended by Deeter and Lor...
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ژورنال
عنوان ژورنال: Surveys in Differential Geometry
سال: 2004
ISSN: 1052-9233,2164-4713
DOI: 10.4310/sdg.2004.v9.n1.a7