Nevanlinna matrices for the strong Stieltjes moment problem

Let ∗cn∗n=−∞∞ be a doubly infinite sequence of real numbers. A solution of the strong Hamburger moment problem is a positive measure σ on (−∞, ∞) such that cn=∫−∞∞ un dδ(u) for n = 0, ±1, ±2,…. A solution of the strong Stieltjes moment problem is a positive measure σ on [0, ∞) such that cn=∫0∞ un dδ(u) for n = 0, +1̄, +2̄,…. A moment problem is indeterminate if there exists more than one solution. With an indeterminate strong Hamburger moment problem there is associated a Nevanlinna matrix of functions α, β, γ, δ holomorphic in ofC − ∗0∗. These functions have growth properties partly similar to properties of analogous entire functions associated with an indeterminate classical Hamburger moment problem. In this paper we obtain a stronger growth result in the case where the strong Stieltjes moment problem is solvable.