On the Non-Commutative Neutrix Product of the Distributions X-r+ Lnp X+ and Xμ+lnq< X+

Tas, KenanFisher, Brian2022-11-252025-09-182022-11-252025-09-182006Fisher, Brian; Taş, Kenan (2006). "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. 513-519.1065-24691476-8291https://doi.org/10.1080/10652460600725283https://hdl.handle.net/123456789/12462Tas, Kenan/0000-0001-8173-453XLet 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+ Lnp X+ and Xμ+lnq< X+On the non-commutative neutrix product of the distributions x(+)(-r) ln(p) x(+) and x(+)(mu)ln(q) x(+)Article10.1080/106524606007252832-s2.0-33745632078