论文标题
非本地Schrödinger运算符的负特征值具有签名势势
Negative eigenvalues of non-local Schrödinger operators with sign-changing potentials
论文作者
论文摘要
Simon在经常性Schrödinger操作员的负面频谱上的结果（$ d = 1,2 $）扩展到更广泛的潜力和非本地运营商。构建了$ l^1- $ potental的一个示例，其中二维Schrödinger操作员的基本频谱覆盖了整个轴。为瞬态运算符（$ d \ geq3 $）提供了一些反例，表明对CWIKEL-LIEB-ROZENBLUM估计的有效性的可能性无法得到显着改善。
Simon's results on the negative spectrum of recurrent Schrödinger operators ($d=1,2$) are extended to a wider class of potentials and to non-local operators. An example of $L^1-$potental is constructed for which the essential spectrum of two-dimensional Schrödinger operator covers the whole axis. Some counterexamples are provided for transient operators ($d\geq3$) showing that the assumptions on the potential for the validity of the Cwikel-Lieb-Rozenblum estimate can't be improved significantly.
