Area Transforms

This paper presents the theory of an operational calculus which is much more general than previously available theories. The theory is essentially all inclusive in that any operational analysis for which there is a multiplicative notion of transfer function for linear time-invariant systems is a special case of the general theory given here. The introduction reviews the foundations of operational analysis and then leads quite naturally to area transforms as the most general form. The general theory given here is conceptually very attractive in that it unites and extends all previous theories. Also, it is adequately general to include functions such as exp in its domain of applicability. The basic idea of the theory is to express the functions of time as the superposition of exponential functions, exp , with the superposition over the entire complex plane rather than over only a line in the plane as done with previously available forms of operational analysis (Fourier, Laplace, and Stieltjes transforms).