Title

Necessary and Sufficient Condition that the Limit of Stieltjes Transforms is a Stieltjes Transform

Author Info

Jeffrey S. Geronimo, Georgia Institute of Technology
Theodore P. Hill, Georgia Institute of Technology - Main CampusFollow

Recommended Citation

Postprint version. Published in Journal of Approximation Theory, Volume 121, January 1, 2003, pages 54-60.

Copyright © 2003 Elsevier.

NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.

The definitive version is available at https://doi.org/10.1016/S0021-9045(02)00042-4.

Abstract

The pointwise limit S of a sequence of Stieltjes transforms (S_n) of real Borel probability measures (P_n) is itself the Stieltjes transform of a Borel p.m. P if and only if iy S(iy) →−1as y →∞, in which case P_n converges to P in distribution. Applications are given to several problems in mathematical physics.

Disciplines

Mathematics