Properties of Laplace-Stieltjes-type integrals - M. M. Sheremeta (Математичні Студії)
The properties of Laplace-Stieltjes-type integrals $I(r)=\int_{0}^{\infty}a(x)f(xr)dF(x)$ are studied, where $F$ is a non-negative non-decreasing unbounded continuous on the right function on $[0,\,+\infty)$, $f(z)=\sum_{k=0}^{\infty}f_kz^k$ is an entire transcendental function with $f_k\ge 0$ for all $k\ge0$, and a function $a(x)\ge 0$ on $[0,\,+\infty)$ is such that the Lebesgue-Stieltjes integral $\int_{0}^{K}a(x)f(xr)dF(x)$ exists for every $r\ge 0$ and $K \in [0,\,+\infty)$.