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Keywords:
distribution; neutrix product; change of variable
distribution; neutrix product; change of variable
Summary:
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 $H(f)$.
References:
[1] van der Corput J.G.: Introduction to the neutrix calculus. J. Analyse Math. 7 (1959-60), 291-398. MR 0124678 | Zbl 0097.10503
[2] Fisher B.: A non-commutative neutrix product of distributions. Math. Nachr. 108 (1982), 117-127. Zbl 0522.46025
[3] Fisher B.: On defining the distribution $\delta ^{(r)}(f(x))$ for summable $f$. Publ. Math. Debrecen 32 (1985), 233-241. MR 0834774
[4] Fisher B.: On the product of distributions and the change of variable. Publ. Math. Debrecen 35 (1988), 37-42. MR 0971950 | Zbl 0668.46015
[5] Fisher B., Özcağ E.: A result on distributions and the change of variable. submitted for publication.
[6] Gel'fand I.M., Shilov G.E.: Generalized Functions. vol. I., Academic Press, 1964. MR 0166596 | Zbl 0159.18301
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