论文标题
均匀的复合时间热内核估计无高斯边界
Uniform Complex Time Heat Kernel Estimates Without Gaussian Bounds
论文作者
论文摘要
在本文中，首先，我们考虑$ e^{ - z（-Δ）^{\fracα{2}}} $的均匀复杂时间加热内核估计值，对于$α> 0，z \ in \ mathbb {c}^+$。当$ \fracα{2} $不是整数时，通常，加热内核doest没有实时的高斯上限。因此，Phragmén-Lindelöf方法无法给出均匀的复杂时间估计。取而代之的是，我们的第一个结果使$ p（z，x）$的渐近估算为$ z $趋向于虚构轴。然后，我们证明了均匀的复杂时间热内核估计值。最后，我们还显示了由$ h =（ - δ）^{\fracα{2}}}+v $生成的分析半群的统一估计值，其中$ v $属于高级订单Kato类。
In this paper, first we consider the uniform complex time heat kernel estimates of $e^{-z(-Δ)^{\fracα{2}}}$ for $α>0, z\in \mathbb{C}^+$. When $\fracα{2}$ is not an integer, generally the heat kernel doest not have the Gaussian upper bounds for real time. Thus the Phragmén-Lindelöf methods fail to give the uniform complex time estimates. Instead, our first result gives the asymptotic estimates for $P(z, x)$ as $z$ tending to the imaginary axis. Then we prove the uniform complex time heat kernel estimates. Finally we also show the uniform estimates of analytic semigroup generated by $H=(-Δ)^{\fracα{2}}+V$ where $V$ belongs to higher order Kato class.
