论文标题
关于某些非本地运算符的两种定量唯一延续结果的方法
On Two Methods for Quantitative Unique Continuation Results for Some Nonlocal Operators
论文作者
论文摘要
在本文中，我们提出了两种用于推论某些积分运算符类别的对数定量延续界限的机制。在我们的第一个方法（扩展相应的积分内核）中，我们利用了瞬间问题的对数稳定性。在我们的第二种方法中，我们依靠某些傅立叶乘数的分支切割奇点的存在。作为一个应用程序，我们提供了操作员$ l_s（d）= \ sum \ limits_ {j = 1}^{n}（ - \ partial_ {x_j}^2）^{s} + q $ with [\ frac frac {1}，$ s oct oct， $ \ Mathbb {r}^n $上的功能。
In this article we present two mechanisms for deducing logarithmic quantitative unique continuation bounds for certain classes of integral operators. In our first method, expanding the corresponding integral kernels, we exploit the logarithmic stability of the moment problem. In our second method we rely on the presence of branch-cut singularities for certain Fourier multipliers. As an application we present quantitative Runge approximation results for the operator $ L_s(D) = \sum\limits_{j=1}^{n}(-\partial_{x_j}^2)^{s} + q$ with $s\in [\frac{1}{2},1)$ and $q\in L^{\infty}$ acting on functions on $\mathbb{R}^n$.
