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

✍ Scribed by Jeffrey S. Geronimo; Theodore P. Hill

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 144 KB
• Volume: 121
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1016/s0021-9045(02)00042-4

✦ Synopsis

The pointwise limit S of a sequence of Stieltjes transforms ðS n Þ of real Borel probability measures ðP n Þ is itself the Stieltjes transform of a Borel p.m. P if and only if iySðiyÞ-À 1 as y-N; in which case P n converges to P in distribution. Applications are given to several problems in mathematical physics.