论文标题
一类SingularSchrödinger操作员的半经典渐近学
Semiclassical asymptotics for a class of singular Schrödinger operators
论文作者
论文摘要
令$ω\ subset \ mathbb {r}^d $用$ c^1 $边界界定。在本文中，我们考虑$ W（x）\ of yathrm {dist}（x，x，\partialΩ）^{ - 2} $作为$ w（x）\ yathrm {distrm {dist}（x，x，x，partialΩ）\至0 $ $。在$ w $的假设下，我们为该运营商特征值的总和提供了两项渐近公式。
Let $Ω\subset \mathbb{R}^d$ be bounded with $C^1$ boundary. In this paper we consider Schrödinger operators $-Δ+ W$ on $Ω$ with $W(x)\approx\mathrm{dist}(x, \partialΩ)^{-2}$ as $\mathrm{dist}(x, \partialΩ)\to 0$. Under weak assumptions on $W$ we derive a two-term asymptotic formula for the sum of the eigenvalues of such operators.
