Necessary and sufficient condition that the limit of Stieltjes transforms is a Stieltjes transform
نویسندگان
چکیده
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) → −1 as y → ∞, in which case Pn converges to P in distribution. Applications are given to several problems in mathematical physics.
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ورودعنوان ژورنال:
- Journal of Approximation Theory
دوره 121 شماره
صفحات -
تاریخ انتشار 2003