Abstract :
The following "rational" moment problem is discussed. Given distinct real numbers λ1, λ2,..., λp (the "poles" of the problem), real numbers c0 and c(i)j (j = 1, 2, 3,...; i = 1, 2,..., p), and a non-empty compact subset K of (− ∞, + ∞), find necessary and sufficient conditions that there exist a non-negative Borel measure μ, supported on K, such that c0 = ∫Kd μ(t) and c(i)j = ∫K(t − λi)−jd μ(t) for j = 1, 2, 3,... and i = 1, 2,..., p.
