Geodesic
On the non-commutative neutrix product $\ln x_+\circ x_+^{-s}$
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 2, pp. 229-239 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $r=s=1$.
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 $r=s=1$.
Classification : 46F10
Keywords: distribution; delta-function; neutrix; neutrix limit; neutrix product 
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     title = {On the non-commutative neutrix product $\ln x_+\circ x_+^{-s}$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {229--239},
     year = {1996},
     volume = {37},
     number = {2},
     mrnumber = {1398998},
     zbl = {0855.46025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1996_37_2_a2/}
}
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Fisher, Brian; Kiliçman, Adem; Damyanov, Blagovest; Ault, J. C. On the non-commutative neutrix product $\ln x_+\circ x_+^{-s}$. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 2, pp. 229-239. http://geodesic.mathdoc.fr/item/CMUC_1996_37_2_a2/