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 $r=s=1$.
@article{118828, author = {Brian Fisher and Adem Kili\c cman and Blagovest Damyanov and J. C. Ault}, title = {On the non-commutative neutrix product $\ln x\_+\circ x\_+^{-s}$}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {37}, year = {1996}, pages = {229-239}, zbl = {0855.46025}, mrnumber = {1398998}, language = {en}, url = {http://dml.mathdoc.fr/item/118828} }
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) pp. 229-239. http://gdmltest.u-ga.fr/item/118828/
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