Further theory of operational calculus on discrete analytic functions

Abstract

In 1966 Hayabara developed an operational calculus on the class of functions discrete analytic in the first quadrant of the discrete plane, This development parallels Mikusinski's operational calculus on the class of real valued functions continuous on [0, infinity). In this dissertation a discrete convolution product is considered which is different from that considered by Hayabara, With respect to this new convolution product an operational calculus is developed similar to Hayabara's. A discrete algebraic derivative for the quotient structure developed by Hayabara is also introduced which is analogous to the algebraic derivative of Mikusinski.