在一个域$Ω\subseteq \mathbb{R}^\mathbf{N}$，我们认为紧凑，Birman-Schwinger型，运营商的形式$\mathbf{T}_{P,\mathfrak{A}}=\mathfrak{A}^*P\mathfrak{A}$，这里$P$是一个奇异的Borel措施$Ω$和$\mathfrak{A}$是一个非临界阶$-l\ne -\mathbf{N}/2$伪微分算子。对于一类这样的运营商，我们得到的估计和一个适当的版本H.Weyl的渐近法律的特征值，与顺序取决于尺寸的测量特性。证明了奇异测度的一个新的估计。对于具有奇异测度$P,P_1,P_2$和负阶伪微分算子$\mathfrak{A},\mathfrak{A}_1,\mathfrak{A}_2$的$P_2 \mathfrak{A} P_1$和$\mathfrak{A}_2 P \mathfrak{A}_1$形式的非自伴算子，我们得到了奇异数的估计.
英文摘要：
In a domain $Ω\subseteq \mathbb{R}^\mathbf{N}$ we consider compact, Birman-Schwinger type, operators of the form $\mathbf{T}_{P,\mathfrak{A}}=\mathfrak{A}^*P\mathfrak{A}$; here $P$ is a singular Borel measure in $Ω$ and $\mathfrak{A}$ is a noncritical order $-l\ne -\mathbf{N}/2$ pseudodifferential operator. For a class of such operators, we obtain estimates and a proper version of H.Weyl's asymptotic law for eigenvalues, with order depending on dimensional characteristics of the measure. A version of the CLR estimate for singular measures is proved. For non-selfadjoint operators of the form $P_2 \mathfrak{A} P_1$ and $\mathfrak{A}_2 P \mathfrak{A}_1$ with singular measures $P,P_1,P_2$ and negative order pseudodifferential operators $\mathfrak{A},\mathfrak{A}_1,\mathfrak{A}_2$ we obtain estimates for singular numbers.
A uniform elliptic reduction, an order-matching criterion, and precision benchmarks for the strong-coupling Birman-Schwinger analysis of the lattice three-boson trimer
Czech Technical University（捷克理工大学）；Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University（捷克理工大学道普勒应用数学物理研究所）；Nuclear Physics Institute, Academy of Sciences（科学院核物理研究所）
Spectral analysis of Dirac operators for dislocated potentials with a purely imaginary jump
Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University（赫瑞-瓦特大学数学系和麦克斯韦数学科学研究所）；Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague（布拉格捷克技术大学核科学与物理工程学院数学系）；Faculty of Mathematics and Statistics, Ton Duc Thang University（胡志明市统一大学数学与统计学院）
