On the construction of Dirichlet series approximations for completely monotone functions (Q2871186)

It has been shown already by Liu that if a function can be approximated arbitrarily close by Dirichlet series with nonnegative coefficients in \(L_{p}\)-norm with \(1 \leq p \leq \infty\) then it follows that it is completely monotonic. This paper is now concerned with the problem to find a constructive procedure to approximate completely monotonic functions which are the Laplace transforms of absolutely continuous finite positive measures. Being able to generate accurate approximations of the Laplace transforms of completely monotonic functions opens the way to obtain approximate solutions for the interconversion relationship of rheology and for the solution of Volterra integral equations of first kind.