论文标题
具有奇异电位的分数型Schrödinger的绑定状态和热内核
Bound states and heat kernels for fractional-type Schrödinger operators with singular potentials
论文作者
论文摘要
我们考虑非本地schrödinger运算符$ h = -l-v $ in $ l^2（\ mathbf {r}^d）$，$ d \ geq 1 $，其中动力学术语$ l $是伪差异的操作员，它们是界面上的非元素的差异laplacian的扰动，而不是界面的非元素运营商和$ $ v $。我们证明了对应于负征负征值和热核上有限的时间范围的特征函数的点估计。我们还分析了匹配的较低估计量的热核与原点附近的基态之间的关系。我们的结果涵盖了具有库仑潜力的相对论施罗丁运营商。
We consider non-local Schrödinger operators $H=-L-V$ in $L^2(\mathbf{R}^d)$, $d \geq 1$, where the kinetic terms $L$ are pseudo-differential operators which are perturbations of the fractional Laplacian by bounded non-local operators and $V$ is the fractional Hardy potential. We prove pointwise estimates of eigenfunctions corresponding to negative eigenvalues and upper finite-time horizon estimates for heat kernels. We also analyze the relation between the matching lower estimates of the heat kernel and the ground state near the origin. Our results cover the relativistic Schrödinger operator with Coulomb potential.
