Fisher, Brian; Taş, Kenan Some results on the non-commutative neutrix product of distributions. (English) Zbl 1171.46031 Integral Transforms Spec. Funct. 20, No. 1, 35-44 (2009). Summary: It is proved that the non-commutative neutrix product of the distributions \(x^{-r}\) and \(x^s \ln ^q|x|\) exists and \[ x^{-r}\circ (x^s \ln^q |x|)=x^{-r+s}\ln^{q}|x| \] for \(r,q=1,2,\dots\), \(s=0,\pm 1,\pm 2,\dots\), \(r-s>1\). Cited in 1 Document MSC: 46F10 Operations with distributions and generalized functions Keywords:distribution; delta-function; neutrix; neutrix limit; neutrix product PDFBibTeX XMLCite \textit{B. Fisher} and \textit{K. Taş}, Integral Transforms Spec. Funct. 20, No. 1, 35--44 (2009; Zbl 1171.46031) Full Text: DOI References: [1] DOI: 10.1093/qmath/22.2.291 · Zbl 0213.13104 · doi:10.1093/qmath/22.2.291 [2] DOI: 10.1002/mana.19800990126 · Zbl 0468.46027 · doi:10.1002/mana.19800990126 [3] DOI: 10.1002/mana.19821080110 · Zbl 0522.46025 · doi:10.1002/mana.19821080110 [4] DOI: 10.1080/1065246042000272018 · Zbl 1075.46035 · doi:10.1080/1065246042000272018 [5] Fisher B., Rad. Mat. 10 pp 85– (2000) [6] Gel’fand, I. M. and Shilov, G. E. 1964. ”Generalized Functions”. Vol. I, New York: Academic Press. [7] van der Corput J. G., J. Anal. Math. 7 pp 291– (1959) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.