Bounds on embedded singular spectrum for one-dimensional Schrödinger operators
Bounds on embedded singular spectrum for one-dimensional Schrödinger operators
复制标题
一维薛定谔算子嵌入奇异谱的界限
DOI：
10.1090/s0002-9939-99-05110-2
复制
发表时间：
1999
影响因子：
1.5
通讯作者：
C. Remling
中科院分区：
文献类型：
--
作者：
C. Remling
本文证明了一维薛定谔方程−y′′ + Vy = Ey的解在能量E ≤ 2（1−α）的Hausdorff维数下满足WKB渐近公式.这一结果对可能的嵌入奇异谱的结构给出了限制。证明依赖于与WKB方法相关联的积分变换的新的范数估计。
We show that the solutions of the one-dimensional Schrödinger equation −y′′ + V y = Ey with potential V (x) = O(x−α) satisfy the WKB asymptotic formulae off a set of energies E of Hausdorff dimension ≤ 2(1−α). This result gives restrictions on the structure of possible embedded singular spectrum. The proof relies on new norm estimates for the integral transform associated with the WKB method.