K∞ generalized functions

Abstract

This paper presents a theory of generalized functions that is much less abstract than the conventional ones. The theory presented is sufficiently general to encompass all singularity functions of the impulsive type without the need for abstract mathematics. Previous work has shown that it is possible to solve lumped linear circuits and other differential systems without leaving the time domain provided that the basic signal set consists of one-sided waveforms that are differentiable an arbitrary number of times. It is shown below that such a signal set can be constructed from the set of all one-sided K∞ waveforms on -∞ < t < ∞.