论文标题
在积极的确定分布上
On positive definite distributions
论文作者
论文摘要
我们为S'（r）$中的回火分配$ f \提供了必要的条件，以确定为正。 $ f $的广义cauchy transform $ \ wideTilde {f} $用作$ f $的数值延续，以$ c $ $ c $的开放式上和下部复合体半平台。实际上，我们对$ f $的必要条件完全取决于$ \ widetilde {f} $对$ c $中假想轴的限制的属性。主要结果是根据完全单调和绝对单调的功能给出的。
We provide necessary and sufficient conditions for a tempered distribution $F\in S'(R)$ to be positive definite. A generalized Cauchy transform $\widetilde{F}$ of $F$ is used as a numerical continuation of $F$ to the open upper and lower complex half-planes in $C$. In fact, our necessary and sufficient conditions for $F$ are determined completely by the properties of the restriction of $\widetilde{F}$ to the imaginary axis in $C$. The main result is given in terms of completely monotonic and absolutely monotonic functions.
