On the Non-Commutative Neutrix Product of the Distributions Xλ+ and Xμ+

Tas, K.Fisher, B.01. Çankaya Üniversitesi2022-11-252025-09-182022-11-252025-09-182006Fisher, B.; Taş, Kenan (2006). "On the non-commutative neutrix product of the distributions x(+)(lambda) and x(+)(mu)", ACTA MATHEMATICA SINICA-ENGLISH SERIES, Vol. 22, No. 6, pp. 1639-1644.1439-85161439-7617https://doi.org/10.1007/s10114-005-0762-7https://hdl.handle.net/20.500.12416/14391Tas, Kenan/0000-0001-8173-453XLet 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 Xλ+ and Xμ+On the non-commutative neutrix product of the distributions x(+)(lambda) and x(+)(mu)Article10.1007/s10114-005-0762-72-s2.0-33749644764