Functions on discrete sets holomorphic in the sense of Ferrand, or monodiffric functions of the second kind (Q943410)

This paper deals with a discrete counterpart to the class of holomorphic functions in one or two complex variables -- in a terminology due to Rufus Philip Isaac's so-called monodiffric functions of the second kind. Discrete analogues of the Cauchy-Riemann operator, of domains of holomorphy in one discrete variable, and of the Hartogs phenomenon in two discrete variables are investigated. Two fundamental solutions to the discrete Cauchy-Riemann equations are studied: one with support in a quadrant, the other with decay at infinity. While the first is easily constructed by induction, the second one can be accessed via its Fourier transform.