On constructing measures from moments
Daniel P. Mäki · Scandinavian Actuarial Journal · 1970
We are interested in the following familiar problem. Given a real sequence µn ∞ 0 find a finite, positive measure a, which is defined on the real line R and for which It is well known that such a measure a does not always exist,. In fact necessary and sufficient conditions for the existence of σ were given by Hamburger in 1920, and they constitute the solution of what is now called the Hamburger moment problem. (See [4] for a general history of the moment problem.) In this paper, we concentrate on the related problem of actually constructing the measure σ. Thus, we consider certain classes of real sequences; and for these sequences we give a description of a and a method of obtaining σ.