论文标题
与连续Schrödinger操作员相关的基督徒功能的渐近学
Asymptotics for Christoffel functions associated to continuum Schrödinger operators
论文作者
论文摘要
我们证明了ContinuumSchrödinger操作员在某些轻度条件下，在频谱度量的某些轻度条件下，ContinuumSchrödinger操作员的基督佛尔函数的渐近学，$λ_l（ξ）$。结果表明，$lλ_l（ξ）$具有限制，并且该限制由radon-nikodym衍生物给出了相对于马丁度量的光谱度量。将其与最近开发的本地标准在规模上$λ_l（ξ）$相结合，我们计算了ContinueSchrödinger运营商的通用性限制，并以$ L $为单位，并获得有限范围截断的特征值的时钟间距。
We prove asymptotics of the Christoffel function, $λ_L(ξ)$, of a continuum Schrödinger operator for points in the interior of the essential spectrum under some mild conditions on the spectral measure. It is shown that $Lλ_L(ξ)$ has a limit and that this limit is given by the Radon--Nikodym derivative of the spectral measure with respect to the Martin measure. Combining this with a recently developed local criterion for universality limits at scale $λ_L(ξ)$, we compute universality limits for continuum Schrödinger operators at scale $L$ and obtain clock spacing of the eigenvalues of the finite range truncations.
