论文标题
没有磁性schrödinger操作员的正征值
Absence of positive eigenvalues of magnetic Schrödinger operators
论文作者
论文摘要
我们研究了足够的条件，这些条件缺乏$ \ mathbb {r}^d，\，d \ geq 2 $中的磁性schrödinger算子的正征值。在我们的主要结果中，我们证明缺乏高于某些阈值能量的特征值，这明确取决于磁场和电场。与米勒（Miller）的示例进行了比较，表明，就磁场的衰减而言，我们的结果很清晰。作为应用程序，我们描述了二维Pauli和Dirac运营商的主要结果以及两个和三维Aharonov-Bohm运营商的几个后果。
We study sufficient conditions for the absence of positive eigenvalues of magnetic Schrödinger operators in $\mathbb{R}^d,\, d\geq 2$. In our main result we prove the absence of eigenvalues above certain threshold energy which depends explicitly on the magnetic and electric field. A comparison with the examples of Miller--Simon shows that our result is sharp as far as the decay of the magnetic field is concerned. As applications, we describe several consequences of the main result for two-dimensional Pauli and Dirac operators, and two and three dimensional Aharonov--Bohm operators.
