There is some gap, in fact I can improve half of the argument of Discrete harmonic function , the pdf version is Discrete harmonic function in Z^n, but I still have some gap to deal with the residue half… 1. The statement of result First of all, we give the definition of discrete harmonic function. Definition 1 (Discrete harmonic function) We say a function $ {f: {\mathbb Z}^n \rightarrow {\mathbb R}}$ is a discrete harmonic function on $ {{\mathbb Z}^n}$ if and only if for any $ {(x_1,…
