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Original Articles

Several results on the commutative neutrix product of distributions

Pages 559-568 | Received 11 Aug 2006, Published online: 13 Aug 2007
 

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.

Additional information

Notes on contributors

C. K. Li

Email: [email protected]

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