论文标题
在关键情况下，具有单数度量的加权假数算子的特征值估计和渐近分差估计值
Eigenvalue estimates and asymptotics for weighted pseudodifferential operators with singular measures in the critical case
论文作者
论文摘要
在域中$ω\ subset \ mathbb {r}^{\ mathbf {n}} $我们考虑一个自adjoint Opitiator $ \ MathBf {t} = \ Mathfrak {a}^*p \ p.p \ Mathfrak {a} $ -l = - \ Mathbf {n}/2 $和$ P =Vμ_σ$是$ω$的单数签名度量，集中在Lipschitz表面$σ$ dimension $ d <\ mathbf {N n} $上，绝对连续地相对于表面措施$μ__σ$ on $σ$。我们为该操作员建立特征值估计和渐近学。事实证明，这些估计和渐近学的顺序与表面的尺寸$ d $无关。如果有几个表面，可能有不同的维度，以及在$ω$上的绝对连续度量，则相应的渐近系数加起来。
In a domain $Ω\subset \mathbb{R}^{\mathbf{N}}$ we consider a selfadjoint operator $\mathbf{T}=\mathfrak{A}^*P\mathfrak{A} ,$ where $\mathfrak{A}$ is a pseudodifferential operator of order $-l=-\mathbf{N}/2$ and $P=Vμ_Σ$ is a singular signed measure in $Ω$ concentrated on a Lipschitz surface $Σ$ of dimension $d<\mathbf{N}$, absolutely continuous with respect to the surface measure $μ_Σ$ on $Σ$. We establish eigenvalue estimates and asymptotics for this operator. It turns out that the order of these estimates and asymptotics is independent of the dimension $d$ of the surface. If there are several surfaces, possibly, of different dimensions, as well as an absolute continuous measure on $Ω$ the corresponding asymptotic coefficients add up.
