Some Results on the Composition of Distributions - Ege, Inci (Sarajevo Journal of Mathematics, 2024)
Let F be a distribution, f be a locally summable function and F_n = (F * δ_n)(x), where δ_n(x) is a certain sequence converging to the Dirac delta-function δ(x). The distribution F(f) is defined as the neutrix limit of the sequence { F_n(f) }, provided its limit h exists in the sense that _-∞^∞ F_n(f(x))φ (x) dx = h(x) , φ (x) a for all test functions φ(x) in D(a,b). The composition of the distributions x_-^-sx_- and x_+^r is evaluated for r=0,1, … and the composition of the distributions x_-^-s^m x_- and H(x) is evaluated for s,m=1,2,… . 2000 Mathematics Subject Classification. 46F10