Necessary and Sufficient Condition that the Limit of Stieltjes Transforms is a Stieltjes Transform (2003)
by
Jeffrey S. Geronimo
,
Theodore P. Hill
| Venue: | J. Approx. Theory |
| Citations: | 7 - 0 self |
BibTeX
@ARTICLE{Geronimo03necessaryand,
author = {Jeffrey S. Geronimo and Theodore P. Hill},
title = {Necessary and Sufficient Condition that the Limit of Stieltjes Transforms is a Stieltjes Transform},
journal = {J. Approx. Theory},
year = {2003},
volume = {121},
pages = {54--60}
}
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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) → -1 as y → ∞, in which case P_n converges to P in distribution. Applications are given to several problems in mathematical physics.
