Necessary and sufficient condition that the limit of Stieltjes transforms is a Stieltjes transform

Authors:
Jeffrey S. Geronimo;Theodore P. Hill
Affiliations:
Georgia Institute of Technology, School of Mathematics, Atlanta, GA;Georgia Institute of Technology, School of Mathematics, Atlanta, GA
Venue:
Journal of Approximation Theory
Year:
2003

Citing 3
Cited 3

Real and complex analysis, 3rd ed.

Real and complex analysis, 3rd ed.
The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients

Journal of Approximation Theory
Advanced Engineering Mathematics: Maple Computer Guide

Advanced Engineering Mathematics: Maple Computer Guide

Recurrence relations and vector equilibrium problems arising from a model of non-intersecting squared Bessel paths

Journal of Approximation Theory
Full length article: Asymptotics for the ratio and the zeros of multiple Charlier polynomials

Journal of Approximation Theory
Full length article: Asymptotics for the ratio and the zeros of multiple Charlier polynomials

Journal of Approximation Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

The 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 iyS(iy) → -1 as y → ∞, in which case Pn converges to P in distribution. Applications are given to several problems in mathematical physics.