论文标题
具有非平滑系数的差分运算符的最佳半经典光谱渐近学
Optimal semiclassical spectral asymptotics for differential operators with non-smooth coefficients
论文作者
论文摘要
我们认为定义为具有非平滑系数的二次形式的Friedrichs扩展。我们证明了这些操作员的Riesz手段的两个任期最佳渐近线，从而在某些规律性条件下谴责了最佳的Weyl定律。然后将使用的方法扩展，以考虑更普遍的可允许的操作员，由粗糙的差分运算符扰动，并在某些规律性条件下再次获得最佳的光谱渐近性。对于Weyl定律，我们假设系数与Hölder连续衍生物可区分，而对于Riesz表示，我们假设系数与Hölder连续衍生物的两倍差异。
We consider differential operators defined as Friedrichs extensions of quadratic forms with non-smooth coefficients. We prove a two term optimal asymptotic for the Riesz means of these operators and thereby also reprove an optimal Weyl law under certain regularity conditions. The methods used are then extended to consider more general admissible operators perturbed by a rough differential operator and obtaining optimal spectral asymptotics again under certain regularity conditions. For the Weyl law we assume the coefficients are differentiable with Hölder continuous derivatives and for the Riesz means we assume the coefficients are two times differentiable with Hölder continuous derivatives.
