On the non-commutative neutrix product
Brian Fisher; Adem Kiliçman; Blagovest Damyanov; J. C. Ault
Commentationes Mathematicae Universitatis Carolinae (1996)
- Volume: 37, Issue: 2, page 229-239
- ISSN: 0010-2628
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topFisher, Brian, et al. "On the non-commutative neutrix product $\ln x_+\circ x_+^{-s}$." Commentationes Mathematicae Universitatis Carolinae 37.2 (1996): 229-239. <http://eudml.org/doc/247883>.
@article{Fisher1996,
abstract = {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 $r=s=1$.},
author = {Fisher, Brian, Kiliçman, Adem, Damyanov, Blagovest, Ault, J. C.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {distribution; delta-function; neutrix; neutrix limit; neutrix product; delta-function; neutrix limit; non-commutative neutrix product; distributions},
language = {eng},
number = {2},
pages = {229-239},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the non-commutative neutrix product $\ln x_+\circ x_+^\{-s\}$},
url = {http://eudml.org/doc/247883},
volume = {37},
year = {1996},
}
TY - JOUR
AU - Fisher, Brian
AU - Kiliçman, Adem
AU - Damyanov, Blagovest
AU - Ault, J. C.
TI - On the non-commutative neutrix product $\ln x_+\circ x_+^{-s}$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 2
SP - 229
EP - 239
AB - 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 $r=s=1$.
LA - eng
KW - distribution; delta-function; neutrix; neutrix limit; neutrix product; delta-function; neutrix limit; non-commutative neutrix product; distributions
UR - http://eudml.org/doc/247883
ER -
References
top- van der Corput J.G., Introduction to the neutrix calculus, J. Analyse Math. 7 (1959-60), 291-398. (1959-60) Zbl0097.10503MR0124678
- Fisher B., The product of distributions, Quart. J. Math. Oxford (2) 22 (1971), 291-298. (1971) Zbl0213.13104MR0287308
- Fisher B., On defining the product of distributions, Math. Nachr. 99 (1980), 239-249. (1980) Zbl0468.46027MR0637662
- Fisher B., A non-commutative neutrix product of distributions, Math. Nachr. 108 (1982), 117-127. (1982) Zbl0522.46025
- Fisher B., Some results on the non-commutative neutrix product of distributions, Trabajos de Matematica 44, Buenos Aires, 1983. Zbl1171.46031
- Fisher B., Kiliçman A., The non-commutative neutrix product of the distributions and , Math. Balkanica 8 (2-3) (1994), 251-258. (1994) MR1338782
- Fisher B., Savaş E., Pehlivan S., Özçağ E., Results on the non-commutative neutrix product of distributions, Math. Balkanica 7 (1993), 347-356. (1993) MR1269889
- Gel'fand I.M., Shilov G.E., Generalized Functions, Vol. I, Academic Press, 1964. Zbl0159.18301MR0166596
- Kiliçman A., Fisher B., On the non-commutative neutrix product , submitted for publication.
- Özçağ E., Fisher B., On defining the distribution , Rostock. Math. Kolloq. 42 (1990), 25-40. (1990) MR1116728
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