1965 Articles

Generalized Sequences with Applications to the Discrete Calculus

Traub, Joseph F.

Mikusinski [17] has introduced a theory of generalized functions which is algebraic in nature. Generalized functions are introduced in a way which is analogous to the extension of the concept of number from integers to rationals. In this paper, an analogous theory of "generalized sequences" is constructed for the discrete calculus. This theory serves a dual purpose. It provides a rigorous foundation for an operational calculus and provides a powerful formalism for the solution of discrete problems.