论文标题
狄拉克 - 库仑运算符，具有一般性电荷分布。 I.区分扩展和最小最大公式
Dirac-Coulomb operators with general charge distribution. I. Distinguished extension and min-max formulas
论文作者
论文摘要
本文是系列中的第一个，我们研究了狄拉克运算符的光谱特性，其库仑电势由任何有限签名的电荷分布产生。我们在这里表明，在唯一条件下，操作员具有独特的杰出自我伴侣扩展，即$μ$没有重量大于或等于1的原子。然后，我们讨论了阳性度量的案例，并使用与上旋转器相关的二次形式来表征该域，此前是Esteban和损失的早期作品。这使我们能够为差距中的特征值提供最小公式。如果某些特征值已经潜入负连续体，则最小公式对于其余的公式仍然有效。在本文的最后，我们还讨论了对应于$μ$的多中心狄拉克-Coulomb操作员的情况。
This paper is the first of a series where we study the spectral properties of Dirac operators with the Coulomb potential generated by any finite signed charge distribution $μ$. We show here that the operator has a unique distinguished self-adjoint extension under the sole condition that $μ$ has no atom of weight larger than or equal to one. Then we discuss the case of a positive measure and characterize the domain using a quadratic form associated with the upper spinor, following earlier works by Esteban and Loss. This allows us to provide min-max formulas for the eigenvalues in the gap. In the event that some eigenvalues have dived into the negative continuum, the min-max formulas remain valid for the remaining ones. At the end of the paper we also discuss the case of multi-center Dirac-Coulomb operators corresponding to $μ$ being a finite sum of deltas.
