| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4617531 | Journal of Mathematical Analysis and Applications | 2012 | 6 Pages |
Abstract
We derive necessary and sufficient conditions for a continuous bounded function f:R→C to be a characteristic function of a probability measure. The Cauchy transform Kf of f is used as analytic continuation of f to the upper and lower half-planes in C. The conditions depend on the behavior of Kf(z) and its derivatives on the imaginary axis in C. The main results are given in terms of completely monotonic and absolutely monotonic functions.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
