论文标题
超级高斯的指数衰减：足够的状态
Super-Gaussian Decay of Exponentials: A Sufficient Condition
论文作者
论文摘要
在本文中，我们为指数$ \ exp（{ - f}）$提出了足够的条件，使尾部衰减比任何高斯都更强，在本地凸出空间$ x $上定义了$ f $，并且比$ x $上的平方seminorm更快。特别是，我们的结果证明了$ \ exp（{ - p（x）^{2+ \ varepsilon}+αq（x）^2}）$对于所有$α，\ varepsilon> 0 $ w.r.t.如果$ p $和$ q $在核空间上进行的ra rad rad ra措施是$ x $的连续eminorms，并具有兼容的内核。这可以看作是Fernique定理的适应性，例如，在量子场理论中具有应用。
In this article, we present a sufficient condition for the exponential $\exp({-f})$ to have a tail decay stronger than any Gaussian, where $f$ is defined on a locally convex space $X$ and grows faster than a squared seminorm on $X$. In particular, our result proves that $\exp({-p(x)^{2+\varepsilon}+αq(x)^2})$ is integrable for all $α,\varepsilon>0$ w.r.t. a Radon Gaussian measure on a nuclear space $X$, if $p$ and $q$ are continuous seminorms on $X$ with compatible kernels. This can be viewed as an adaptation of Fernique's theorem and, for example, has applications in quantum field theory.
