Discrete generalized functions

Abstract

In 1965, Duffin described properties of discrete functions. In this dissertation, integrals defined by Duffin are used to develop a theory of discrete generalized functions. This development parallels the development of conventional generalized functions by Lighthill. Applications of the discrete generalized function theory to the study of operators are described. It is also shown that certain difference equations may be solved by methods adopted from the study of discrete generalized functions.