论文标题
关于特征函数的分析延续的注释
A note on analytic continuation of characteristic functions
论文作者
论文摘要
我们为连续有限函数$ f：r \至c $得出必要和充分的条件，以成为概率度量的特征功能。 $ f $的Cauchy Transform $ k_f $用作$ f $的分析延续，以$ c $为上半平面。条件取决于$ k_f（z）$及其在$ c $中假想轴上的衍生物的行为。主要结果是根据完全单调和绝对单调的功能给出的。
We derive necessary and sufficient conditions for a continuous bounded function $f: R\to C$ to be a characteristic function of a probability measure. The Cauchy transform $K_f$ 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 $K_f(z)$ and its derivatives on the imaginary axis in $C$. The main results are given in terms of completely monotonic and absolutely monotonic functions.
