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Physical Sciences and Mathematics Commons

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California Polytechnic State University, San Luis Obispo

Research Scholars in Residence

Series

2003

Articles 1 - 1 of 1

Full-Text Articles in Physical Sciences and Mathematics

Necessary And Sufficient Condition That The Limit Of Stieltjes Transforms Is A Stieltjes Transform, Jeffrey S. Geronimo, Theodore P. Hill Jan 2003

Necessary And Sufficient Condition That The Limit Of Stieltjes Transforms Is A Stieltjes Transform, Jeffrey S. Geronimo, Theodore P. Hill

Research Scholars in Residence

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