| Title:
|
On the non-commutative neutrix product $\ln x_+\circ x_+^{-s}$ (English) |
| Author:
|
Fisher, Brian |
| Author:
|
Kiliçman, Adem |
| Author:
|
Damyanov, Blagovest |
| Author:
|
Ault, J. C. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
229-239 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The non-commutative neutrix product of the distributions $\ln x_+$ and $x_+^{-s} $ is proved to exist for $s=1,2, \ldots$ and is evaluated for $s=1,2$. The existence of the non-commutative neutrix product of the distributions $x_+^{-r}$ and $x_+ ^{-s}$ is then deduced for $r,s= 1,2, \ldots$ and evaluated for $r=s=1$. (English) |
| Keyword:
|
distribution |
| Keyword:
|
delta-function |
| Keyword:
|
neutrix |
| Keyword:
|
neutrix limit |
| Keyword:
|
neutrix product |
| MSC:
|
46F10 |
| idZBL:
|
Zbl 0855.46025 |
| idMR:
|
MR1398998 |
| . |
| Date available:
|
2009-01-08T18:23:18Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118828 |
| . |
| 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.: The product of distributions.Quart. J. Math. Oxford (2) 22 (1971), 291-298. Zbl 0213.13104, MR 0287308 |
| Reference:
|
[3] Fisher B.: On defining the product of distributions.Math. Nachr. 99 (1980), 239-249. Zbl 0468.46027, MR 0637662 |
| Reference:
|
[4] Fisher B.: A non-commutative neutrix product of distributions.Math. Nachr. 108 (1982), 117-127. Zbl 0522.46025 |
| Reference:
|
[5] Fisher B.: Some results on the non-commutative neutrix product of distributions.Trabajos de Matematica 44, Buenos Aires, 1983. Zbl 1171.46031 |
| Reference:
|
[6] Fisher B., Kiliçman A.: The non-commutative neutrix product of the distributions $x_+ ^{-r}$ and $x_- ^{-s}$.Math. Balkanica 8 (2-3) (1994), 251-258. MR 1338782 |
| Reference:
|
[7] Fisher B., Savaş E., Pehlivan S., Özçağ E.: Results on the non-commutative neutrix product of distributions.Math. Balkanica 7 (1993), 347-356. MR 1269889 |
| Reference:
|
[8] Gel'fand I.M., Shilov G.E.: Generalized Functions.Vol. I, Academic Press, 1964. Zbl 0159.18301, MR 0166596 |
| Reference:
|
[9] Kiliçman A., Fisher B.: On the non-commutative neutrix product $(x_+ ^r \ln x_+) \circ x_- ^{-s} $.submitted for publication. |
| Reference:
|
[10] Özçağ E., Fisher B.: On defining the distribution $x_+ ^{-r} \ln ^s x_+$.Rostock. Math. Kolloq. 42 (1990), 25-40. MR 1116728 |
| . |
