Rational Moment Problems for Compact Sets Original Research Article

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.