On the Noncommutative Neutrix Product of Distributions

Emin Özçaḡ, İnci Ege, Haşmet Gürçay and Biljana Jolevska-Tuneska

Abstract and Applied Analysis, 2007, vol. 2007, issue 1

Abstract: Let f and g be distributions and let gn = (g*δn)(x), where δn(x) is a certain sequence converging to the Dirac‐delta function δ(x). The noncommutative neutrix product f∘g of f and g is defined to be the neutrix limit of the sequence {fgn}, provided the limit h exists in the sense that N‐limn→∞〈f(x)gn(x), φ(x)〉 = 〈h(x), φ(x)〉, for all test functions in 𝒟. In this paper, using the concept of the neutrix limit due to van der Corput (1960), the noncommutative neutrix products x+rlnx+∘x−−r−1lnx− and x−−r−1lnx−∘x+rlnx+ are proved to exist and are evaluated for r = 1, 2, …. It is consequently seen that these two products are in fact equal.

Date: 2007
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https://doi.org/10.1155/2007/81907

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2007:y:2007:i:1:n:081907

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