Discrete geometric function theory !

Abstract

The foundations are laid here for a discrete analytic function theory which can be applied to geometric difference (or q-difference) functions. Using the concept of a q-analytic function. a discrete contour integral is defined and analogues are found for Cauchy integral theorems. Appropriate discrete analytic continuation and multiplication operators are outlined and their properties examined. The development of the theory of q-analytic functions is seen to be closely allied to that monodiffric functions, but significant advantages and distinctive differences are noted