论文标题
改善了径向电势的分解边界。 ii
Improved resolvent bounds for radial potentials. II
论文作者
论文摘要
我们证明了r d，d $ \ ge $ 3中的schr {Ö} dinger操作员的半经典分解估计，并具有实值的径向电势v $ \ in $ l $ \ infty $（r d）。我们表明，如果v（x）= o x- $δ$带有$δ$> 4，则分辨率的限制是exp ch-$Δ$δ$δ$ -1 log -1 log（h -1）1 $δ$ -1，带有常数c> 0。
We prove semiclassical resolvent estimates for the Schr{ö}dinger operator in R d , d $\ge$ 3, with real-valued radial potentials V $\in$ L $\infty$ (R d). We show that if V (x) = O x --$δ$ with $δ$ > 4, then the resolvent bound is of the form exp Ch -- $δ$ $δ$--1 log(h --1) 1 $δ$--1 with some constant C > 0. If V (x) = O e -- C x $α$ with C, $α$ > 0, we get better resolvent bounds of the form exp Ch --1 log(h --1
