论文标题
负特征值的积累速率为零和绝对连续的频谱
The rate of accumulation of negative eigenvalues to zero and the absolutely continuous spectrum
论文作者
论文摘要
对于$ {\ bbb r}^d $上的有限的实价$ v $，我们考虑两个schrödinger运算符$ h _+= - δ+v $和$ h _- = - Δ-δ-v $。我们证明，如果负光谱$ h _ _+$和$ h _- $是离散的，而$ h _+$和$ h _- $的负特征值往往很快零，则 绝对连续的光谱覆盖了正期$ [0，\ infty）$。
For a bounded real-valued function $V$ on ${\Bbb R}^d$, we consider two Schrödinger operators $H_+=-Δ+V$ and $H_-=-Δ-V$. We prove that if the negative spectra $H_+$ and $H_-$ are discrete and the negative eigenvalues of $H_+$ and $H_-$ tend to zero sufficiently fast, then the absolutely continuous spectra cover the positive half-line $[0,\infty)$.
