论文标题
关于绿色功能的消失，降低和卡尔曼的方法
On the vanishing of Green's function, desingularization and Carleman's method
论文作者
论文摘要
本文的主题是在$ \ Mathbb r^3 $上在潜在的$ v $具有积极的关键奇点的位置上$-Δ+ v $消失的现象。更确切地说，对$ v $（即形式结合的性）施加最小的假设，我们在消失的绿色功能的顺序上获得了上限。作为我们证明的副产品，我们改善了$-Δ+ v $ dimension $ d = 3 $的特征函数的强烈独特延续的现有结果。
The subject of the present paper is the phenomenon of vanishing of the Green function of the operator $-Δ+ V$ on $\mathbb R^3$ at the points where a potential $V$ has positive critical singularities. More precisely, imposing minimal assumptions on $V$ (i.e. the form-boundedness), we obtain an upper bound on the order of vanishing of the Green function. As a by-product of our proof, we improve the existing results on the strong unique continuation for eigenfunctions of $-Δ+ V$ in dimension $d=3$.
