Necessary and Sufficient Condition that the Limit of Stieltjes Transforms is a Stieltjes TransformJournal of Approximation Theory
AbstractThe pointwise limit S of a sequence of Stieltjes transforms (Sn) of real Borel probability measures (Pn) is itself the Stieltjes transform of a Borel p.m. P if and only if iy S(iy) →−1as y →∞, in which case Pn converges to P in distribution. Applications are given to several problems in mathematical physics.
Citation InformationJeffrey S. Geronimo and Theodore P. Hill. "Necessary and Sufficient Condition that the Limit of Stieltjes Transforms is a Stieltjes Transform" Journal of Approximation Theory Vol. 121 (2003) p. 54 - 60
Available at: http://works.bepress.com/tphill/56/