论文标题
光谱函数的完整渐近扩展，用于几乎周期性schrödinger操作员的符号扰动。
Complete asymptotic expansions of the spectral function for symbolic perturbations of almost periodic Schrödinger operators in dimension one
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学。令$ p：l^2（\ mathbb {r}）\ to l^2（\ mathbb {r}）$具有$$ p：= - \ tfrac {d^2} {dx^2} {dx^2}+w，$ w，其中$ w $ w $是一个自adexhapine w $ as自adexhaptifexhotagine wend as a sefactaint offainewhotage Dride二阶差异操作员，具有某些修改后的几乎经过定期的定期结构。我们表明，光谱投影仪的内核，$ \ mathbb {1} _ {（ - \ infty，λ^2]}（p）$具有$λ$的权力的完全渐近扩展。尤其是，我们的潜力$ w $在正式的范围内稳定的一类潜在的稳定范围稳定了与某些阶段的互动，与某些阶段的互动式互动相关，这些阶段的互补效率包括在某些方面的范围内，并以某些阶层的态度稳定，这些阶段的运算均稳定，这些阶段的运行式均匀的互助者，这些阶段的态度，这些阶段的态度，这些阶层的态度，这些阶段的态度，这些阶段的运作方式，以及与某些阶层的互动式，这些阶段的态度均匀，并稳定。使用密集的纯点光谱。
In this article we consider asymptotics for the spectral function of Schrödinger operators on the real line. Let $P:L^2(\mathbb{R})\to L^2(\mathbb{R})$ have the form $$ P:=-\tfrac{d^2}{dx^2}+W, $$ where $W$ is a self-adjoint first order differential operator with certain modified almost periodic structure. We show that the kernel of the spectral projector, $\mathbb{1}_{(-\infty,λ^2]}(P)$ has a full asymptotic expansion in powers of $λ$. In particular, our class of potentials $W$ is stable under perturbation by formally self-adjoint first order differential operators with smooth, compactly supported coefficients. Moreover, it includes certain potentials with dense pure point spectrum. The proof combines the gauge transform methods of Parnovski-Shterenberg and Sobolev with Melrose's scattering calculus.
