On the non-commutative neutrix product of the distributions x(+)(lambda) and x(+)(mu)

Taş, KenanFisher, BrianTaş, Kenan2020-04-102020-04-102006Fisher, B; Taş, Kenan, "On the non-commutative neutrix product of the distributions x(+)(lambda) and x(+)(mu)", Acta Mathematica Sinica-English Series, Vol.22, No.6, pp.1639-1644, (2006).1439-8516https://hdl.handle.net/20.500.12416/3051Let f and g be distributions and let 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 circle g of f and g is defined to be the limit of the sequence {fg(n)}, provided its limit h exists in the sense that [GRAPHICS] for all functions p in D. It is proved that (x(+)(lambda)ln(p)x(+)) circle (x(+)(mu)ln(q)x(+)) = x(+)(lambda+mu)ln(p+q)x(+), (x(-)(lambda)ln(p)x(-)) circle (x(-)mu ln(q)x(-)) = x(-)(lambda+mu)ln(p+q)x(-), for lambda + mu < -1; lambda,mu,lambda+mu not equal -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(+)(lambda) and x(+)(mu)On the Non-Commutative Neutrix Product of the Distributions X(+)(Lambda) and X(+)(Mu)Article2261639164410.1007/s10114-005-0762-7