Fisher, Brian; Kuan, Li Chen A commutative neutrix convolution product of distributions. (English) Zbl 0821.46050 Zb. Rad., Prir.-Mat. Fak., Univ. Novom Sadu, Ser. Mat. 23, No. 1, 13-27 (1993). Summary: Let \(f\) and \(g\) be distributions in \({\mathcal D}'\) and let \[ f_ n(x)= f(x) \tau_ n(x),\quad g_ n(x)= g_ n(x) \tau_ n(x), \] where \(\tau_ n(x)\) is a certain function which converges to the identity function as \(n\) tends to infinity. Then the neutrix convolution product \(f\boxed{*} g\) is defined as the neutrix limit of the sequence \(\{f_ n * g_ n\}\), provided the limit \(h\) exists in the sense that \[ N- \lim_{n\to \infty} \langle f_ n * g_ n, \phi\rangle= \langle h, \phi\rangle \] for all \(\phi\) in \(\mathcal D\). The neutrix convolution products \(x^ \lambda_ - \boxed{*} x^ n_ +\) for \(\lambda, \mu,\lambda+ \mu\neq 0\), \(\pm 1,\pm 2,\dots\) and \(x^ \lambda_ -\boxed{*} x^ s_ +\) for \(\lambda\neq 0\), \(\pm 1, \pm 2,\dots\) and \(s= 0, 1, 2,\dots\) are evaluated, from which other neutrix convolution products are deduced. Cited in 1 ReviewCited in 1 Document MSC: 46F10 Operations with distributions and generalized functions Keywords:neutrix convolution product PDFBibTeX XMLCite \textit{B. Fisher} and \textit{L. C. Kuan}, Zb. Rad., Prir.-Mat. Fak., Univ. Novom Sadu, Ser. Mat. 23, No. 1, 13--27 (1993; Zbl 0821.46050)