Abstract
Let H(x) denote Heaviside's function. The goal of this paper is to evaluate the commutative neutrix products f + (x) ⋄ δ(r) (x) and f − (x) ⋄ δ(r) (x) for r=0, 1, 2, …, where f(x) is only the r-th differentiable on an open interval containing the origin and f + (x)=H(x)f(x) and f − (x)=H(−x)f(x). We also obtain the products (ψ (x)/x) ⋄ δ (x), including a few examples as well as x + −r−(1/2) ⋄ x − −r−(1/2).
Acknowledgements
The author is grateful to Dr. Brian Fisher who made several productive suggestions, which improved the quality of this paper. This research is supported by NSERC and BURC.