Some results on the product of distributions
Published online by Cambridge University Press: 24 October 2008
Extract
The product of two distributions f and g on the open interval (a, b), where −∞ ≤ a < b ≤ ∞, was defined(1) as the limit of the sequence {fngn}, provided this sequence is regular on (a, b), where
for n = 1, 2, … and ρ is a fixed infinitely differentiable function having the following properties:
(1) ρ(x) = 0 for |x| ≥ 1,
(2) ρ(x) ≥ 0,
(3) ρ(x) = ρ(−x),
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 2 , March 1973 , pp. 317 - 325
- Copyright
- Copyright © Cambridge Philosophical Society 1973
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