具有任意径向增长的位势在无穷远处的唯一延拓
Unique continuation at infinity for potentials with arbitrary radial growth
AI总结：
针对Rⁿ上Δu=Vu的径向位势V，证明了Landis型定理，构造了由G显式确定的衰减阈值，其指数在合适条件下与Agmon距离成正比，拓展了无穷远处的唯一延拓理论。
AI中文摘要：
设G是R+上任意给定的连续正函数，V是径向函数且满足|V(x)|≤G(|x|)。我们对Rⁿ上Δu=Vu的任意实值解证明了一个Landis型定理，构造了衰减阈值e^(-g(r))，其中g是可由G显式计算的严格递增函数；在合适假设下，该衰减阈值的指数与G相关的Agmon距离成正比。
英文摘要：
Let $G$ be any given continuous positive function on $\mathbb{R}_+$. Let $V$ be radial with $|V(x)|\leq G(|x|)$. We prove a Landis-type theorem for any real-valued solution of $Δu=Vu$ on $\mathbb{R}^n$. We construct a decay threshold $e^{-g(r)}$, where $g$ is a strictly increasing function which can be computed explicitly in terms of $G$. Under suitable assumptions the exponent in the decay threshold is proportional to the Agmon distance associated with $G$.
