论文标题
非本地Schrödinger操作员在潜在和应用方面的基态特征值的稳定性
Stability of ground state eigenvalues of non-local Schrödinger operators with respect to potentials and applications
论文作者
论文摘要
在本文的第一部分中，我们研究了一类非局部Schrödinger操作员的连续性（稳定性）在改变电势方面。通过对电位序列的收敛性施加不同的强度条件，我们给出了直接证明，以显示非局部Schrödinger运算符的强烈或规范的分解收敛，或者通过$γ$ - 连接相关的阳性形式的$γ$ convergence，以提供更多粗糙的电位。在第二部分中，我们使用这些结果通过一系列适当构造的近似因素来显示，具有球形势孔的庞大或无质量相对论的schrödinger算子的基础状态正在质量降低功能。
In a first part of this paper we investigate the continuity (stability) of the spectrum of a class of non-local Schrödinger operators on varying the potentials. By imposing conditions of different strength on the convergence of the sequence of potentials, we give either direct proofs to show the strong or norm resolvent convergence of the so-obtained sequence of non-local Schrödinger operators, or via $Γ$-convergence of the related positive forms for more rough potentials. In a second part we use these results to show via a sequence of suitably constructed approximants that the ground states of massive or massless relativistic Schrödinger operators with spherical potential wells are radially decreasing functions.
