| Title:
|
Some results on the product of distributions and the change of variable (English) |
| Author:
|
Özçag, Emin |
| Author:
|
Fisher, Brian |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
677-685 |
| . |
| Category:
|
math |
| . |
| 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 $H(f)$. (English) |
| Keyword:
|
distribution |
| Keyword:
|
neutrix product |
| Keyword:
|
change of variable |
| MSC:
|
46F10 |
| idZBL:
|
Zbl 0761.46024 |
| idMR:
|
MR1159814 |
| . |
| Date available:
|
2009-01-08T17:48:05Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118447 |
| . |
| Reference:
|
[1] van der Corput J.G.: Introduction to the neutrix calculus.J. Analyse Math. 7 (1959-60), 291-398. Zbl 0097.10503, MR 0124678 |
| Reference:
|
[2] Fisher B.: A non-commutative neutrix product of distributions.Math. Nachr. 108 (1982), 117-127. Zbl 0522.46025 |
| Reference:
|
[3] Fisher B.: On defining the distribution $\delta ^{(r)}(f(x))$ for summable $f$.Publ. Math. Debrecen 32 (1985), 233-241. MR 0834774 |
| Reference:
|
[4] Fisher B.: On the product of distributions and the change of variable.Publ. Math. Debrecen 35 (1988), 37-42. Zbl 0668.46015, MR 0971950 |
| Reference:
|
[5] Fisher B., Özcağ E.: A result on distributions and the change of variable.submitted for publication. |
| Reference:
|
[6] Gel'fand I.M., Shilov G.E.: Generalized Functions.vol. I., Academic Press, 1964. Zbl 0159.18301, MR 0166596 |
| . |
