Iterated Stieltjes transform of generalized functions
The generalized \(S_ 2\)-transform of a member of f of a certain space of generalized functions is defined as \(F(x)=<f(t),K(x,t;\rho)>\), where \[ K(x,t;\rho)=\int^{\infty}_{0}\frac{1}{(x+y)^{\rho}(y+t)^{\rho}}dy, \quad \rho >1/2,\quad 0<x<\infty \quad and\quad 0<t<\infty. \] An inversion theorem for the transform is established interpreting the convergence in the weak distributional sense.
convergence in the weak distributional sense
scientific article; zbMATH DE number 3939995