On the non-commutative neutrix product of the distributions x(+)(-r) ln(p) x(+) and x(+)(mu)ln(q) x(+)

Taş, KenanFisher, BrianTaş, KenanMatematik2020-04-102020-04-102006Fisher, Brian; Taş, Kenan, "On the non-commutative neutrix product of the distributions x(+)(-r) ln(p) x(+) and x(+)(mu)ln(q) x(+)", Integral Transforms And Special Functions, Vol.17, No.7, pp.513-519, (2006).1065-2469https://hdl.handle.net/20.500.12416/3052Let f and g be distributions and g(n) = (g*delta(n))(x), where delta(n)(x ) is a certain sequence converging to the Dirac delta-function. The non-commutative neutrix product f o g of f and g is defined to be the neutrix limit of the sequence {fg(n) }, provided its limit h exists in the sense that [GRAPHICS] for all functions phi in D. It is proved that (x(+)(-r) ln(p) x(+)) o (x(+)(mu) ln(q) x(+)) = x(+)(-r+mu) ln(p+q) x(+) (x(-)(-r) ln(p) (x)-) o (x(-)(mu) ln(q) x(-)) = x(-)(-r+mu) ln(p+q) x(-) for mu < r - 1;mu not equal 0, +/- 1, +/- 2,..., r = 1,2,..., and p, q = 0, 1, 2,....eninfo:eu-repo/semantics/closedAccessDistributionDelta-FunctionProduct Of DistributionsOn the non-commutative neutrix product of the distributions x(+)(-r) ln(p) x(+) and x(+)(mu)ln(q) x(+)On the Non-Commutative Neutrix Product of the Distributions X(+)(-R) Ln(P) X(+) and X(+)(Mu)ln(Q) X(+)Article17751351910.1080/10652460600725283