The noncommutative neutrix product of x--slnm x- and x+r

Mongkolsery Lin; Somsak Orankitjaroen; Brian Fisher

doi:10.1142/S1793557114500429

The noncommutative neutrix product of x_-^-sln^m x_- and x₊^r

Mongkolsery Lin
, Somsak Orankitjaroen
, Brian Fisher

Mahidol University
Universiry of Leicester

Research output: Contribution to journal › Article › peer-review

Abstract

In distribution theory, the product of two distributions can only be defined under certain conditions. In this paper, by using Fisher's definition, it is proved that if G_m,s(x) denotes the distribution (ln^m+1x_-)^(s), then the noncommutative neutrix product G_{m, s}(x) o x₊^r exists and (Equation Presented) for m, s ≤ 1, where c_{r, m} = ∫₀¹x^rln^mxρ^(r)(x)dx. Related neutrix products are then deduced.

Original language	English
Article number	1450042
Journal	Asian-European Journal of Mathematics
Volume	7
Issue number	3
DOIs	https://doi.org/10.1142/S1793557114500429
Publication status	Published - 23 Sept 2014
Externally published	Yes

Keywords

Dirac delta-function
Distribution
neutrix
neutrix limit
neutrix product

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10.1142/S1793557114500429

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title = "The noncommutative neutrix product of x--slnm x- and x+r",

abstract = "In distribution theory, the product of two distributions can only be defined under certain conditions. In this paper, by using Fisher's definition, it is proved that if Gm,s(x) denotes the distribution (lnm+1x-)(s), then the noncommutative neutrix product Gm, s(x) o x+r exists and (Equation Presented) for m, s ≤ 1, where cr, m = ∫01xrlnmxρ(r)(x)dx. Related neutrix products are then deduced.",

keywords = "Dirac delta-function, Distribution, neutrix, neutrix limit, neutrix product",

author = "Mongkolsery Lin and Somsak Orankitjaroen and Brian Fisher",

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Y1 - 2014/9/23

N2 - In distribution theory, the product of two distributions can only be defined under certain conditions. In this paper, by using Fisher's definition, it is proved that if Gm,s(x) denotes the distribution (lnm+1x-)(s), then the noncommutative neutrix product Gm, s(x) o x+r exists and (Equation Presented) for m, s ≤ 1, where cr, m = ∫01xrlnmxρ(r)(x)dx. Related neutrix products are then deduced.

AB - In distribution theory, the product of two distributions can only be defined under certain conditions. In this paper, by using Fisher's definition, it is proved that if Gm,s(x) denotes the distribution (lnm+1x-)(s), then the noncommutative neutrix product Gm, s(x) o x+r exists and (Equation Presented) for m, s ≤ 1, where cr, m = ∫01xrlnmxρ(r)(x)dx. Related neutrix products are then deduced.

KW - Dirac delta-function

KW - Distribution

KW - neutrix

KW - neutrix limit

KW - neutrix product

UR - https://www.scopus.com/pages/publications/85028195952

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The noncommutative neutrix product of x_-^-sln^m x_- and x₊^r

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Keywords

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