The convolution x-r*xs
Glasgow mathematical journal, Tome 17 (1976) no. 1, pp. 53-56
Voir la notice de l'article provenant de la source Cambridge University Press
In a recent paper [1], Jones extended the definition of the convolution of distributions so that further convolutions could be defined. The convolution w1*w2 of two distributions w1 and w2 was defined as the limit ofithe sequence {wln*w2n}, provided the limit w exists in the sense thatfor all fine functions ф in the terminology of Jones [2], wherew1n(x) = wl(x)τ(x/n), W2n(x) = w2(x)τ(x/n)and τ is an infinitely differentiable function satisfying the following conditions:(i) τ(x) = τ(—x),(ii)0 ≤ τ (x) ≤ l,(iii)τ (x) = l for |x| ≤ 1⁄2,(iv) τ (x) = 0 for |x| ≥ 1.
Fisher, B. The convolution x-r*xs. Glasgow mathematical journal, Tome 17 (1976) no. 1, pp. 53-56. doi: 10.1017/S001708950000272X
@article{10_1017_S001708950000272X,
author = {Fisher, B.},
title = {The convolution x-r*xs},
journal = {Glasgow mathematical journal},
pages = {53--56},
year = {1976},
volume = {17},
number = {1},
doi = {10.1017/S001708950000272X},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708950000272X/}
}
[1] 1.Jones, D. S., The convolution of generalized functions, Quart. J. of Math. (Oxford) (2), 24 (1973), 145–163. Google Scholar
[2] 2.Jones, D. S., Generalized functions (McGraw-Hill, 1966). Google Scholar
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