Methods for constructing linear difference operators which simulate analyticity^†

^†This work was partially supported by a Lamar University Summer Research Grant

Abstract

Two methods of construction are presented for obtaining families of linear difference operators simulating the operator . These operators are then applied to suggest the construction of corresponding discrete analogues of Laplace's harmonic operator . Other applications include the generation of additional solutions of the linear difference equations under consideration via indefinite discrete line integrals. The results may also be viewed as extensions of monodiffric and discrete analytic function theories

^†This work was partially supported by a Lamar University Summer Research Grant

^†This work was partially supported by a Lamar University Summer Research Grant

Notes

^†This work was partially supported by a Lamar University Summer Research Grant