论文标题
严格的卷积力凹陷
Strict power concavity of a convolution
论文作者
论文摘要
我们为在$ \ mathbb {r}^n \ times（0，+\ infty）$上定义的函数的卷积变量中的严格抛物线功率凹陷提供了足够的条件。 Since the strict parabolic power concavity of a function defined on $\mathbb{R}^n \times (0,+\infty)$ naturally implies the strict power concavity of a function defined on $\mathbb{R}^n$, our sufficient condition implies the strict power concavity of the convolution of two functions defined on $\mathbb{R}^n$.作为应用程序，我们显示了高斯太空变量中严格的抛物线功率凹陷和严格的功率凹陷 - Weierstass积分和上半空间的泊松组成部分。
We give a sufficient condition for the strict parabolic power concavity of the convolution in space variable of a function defined on $\mathbb{R}^n \times (0,+\infty)$ and a function defined on $\mathbb{R}^n$. Since the strict parabolic power concavity of a function defined on $\mathbb{R}^n \times (0,+\infty)$ naturally implies the strict power concavity of a function defined on $\mathbb{R}^n$, our sufficient condition implies the strict power concavity of the convolution of two functions defined on $\mathbb{R}^n$. As applications, we show the strict parabolic power concavity and strict power concavity in space variable of the Gauss--Weierstass integral and the Poisson integral for the upper half-space.
