Some results on the product of distributions and the change of variable
Özçag, Emin ; Fisher, Brian
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991), p. 677-685 / Harvested from Czech Digital Mathematics Library

Let $F$ and $G$ be distributions in $\Cal D'$ and let $f$ be an infinitely differentiable function with $f'(x)>0$, (or $<0$). It is proved that if the neutrix product $F\circ G$ exists and equals $H$, then the neutrix product $F(f)\circ G(f)$ exists and equals $H(f)$.

Publié le : 1991-01-01
Classification:  46F10
@article{118447,
     author = {Emin \"Oz\c cag and Brian Fisher},
     title = {Some results on the product of distributions and the change of variable},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {32},
     year = {1991},
     pages = {677-685},
     zbl = {0761.46024},
     mrnumber = {1159814},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118447}
}
Özçag, Emin; Fisher, Brian. Some results on the product of distributions and the change of variable. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 677-685. http://gdmltest.u-ga.fr/item/118447/

Van Der Corput J.G. Introduction to the neutrix calculus, J. Analyse Math. 7 (1959-60), 291-398. (1959-60) | MR 0124678 | Zbl 0097.10503

Fisher B. A non-commutative neutrix product of distributions, Math. Nachr. 108 (1982), 117-127. (1982) | Zbl 0522.46025

Fisher B. On defining the distribution $\delta ^{(r)}(f(x))$ for summable $f$, Publ. Math. Debrecen 32 (1985), 233-241. (1985) | MR 0834774

Fisher B. On the product of distributions and the change of variable, Publ. Math. Debrecen 35 (1988), 37-42. (1988) | MR 0971950 | Zbl 0668.46015

Fisher B.; Özcağ E. A result on distributions and the change of variable, submitted for publication.

Gel'Fand I.M.; Shilov G.E. Generalized Functions, vol. I., Academic Press, 1964. | MR 0166596 | Zbl 0159.18301