论文标题
经典波浪方法和现代量规变换：一维情况下的光谱渐近学
Classical Wave methods and modern gauge transforms: Spectral Asymptotics in the one dimensional case
论文作者
论文摘要
在本文中，我们考虑了Schrödinger操作员在实际线路上的光谱函数的渐近行为。令$ h：l^2（\ mathbb {r}）\ to l^2（\ mathbb {r}）$具有$$ h：= - \ frac {d^2} {dx^2}+v，$ v $的$ h：= - \ frac {d^2} {dx^2}+v，其中，其中$ v $是正式的自动化第一订单的差异差异，与平稳的系数搭配ALLEFEFTIVENT，deriv。我们表明，光谱投影仪的内核，$ \ mathbb {1} _ {（ - \ infty，ρ^2]}（h）$，具有$ρ$的全部渐近扩展。这可以解决最后两位作者提出的一项猜想的一维情况。
In this article, we consider the asymptotic behaviour of the spectral function of Schrödinger operators on the real line. Let $H: L^2(\mathbb{R})\to L^2(\mathbb{R})$ have the form $$ H:=-\frac{d^2}{dx^2}+V, $$ where $V$ is a formally self-adjoint first order differential operator with smooth coefficients, bounded with all derivatives. We show that the kernel of the spectral projector, $\mathbb{1}_{(-\infty,ρ^2]}(H)$, has a complete asymptotic expansion in powers of $ρ$. This settles the 1-dimensional case of a conjecture made by the last two authors.
