设$$L_0=\suml_{j=1}^nM_j^0D_j+M_0^0,\,\,\,\,D_j=\frac{1}{i}\frac{\pa}{\paxj},
\quad x\in\Rn,$$是一阶常系数偏微分系统，其中矩阵$M_j^0$是Hermitian矩阵.假设齐次部分是强传播的。在非齐次的情况下，假设算子是各向同性的。阐述了这类系统的谱理论及其潜在的扰动，得到了阈值范围内的极限吸收原理。特别注意的是狄拉克和麦克斯韦算子的详细研究。阈值附近的光谱导数的估计是基于慢度表面上的详细迹线估计。这些估计的两个应用：\begin{itemize}
\item Global spacetime estimates of the associated evolution unitary groups, that are also commonly viewed as decay estimates. In particular the Dirac and Maxwell systems are explicitly treated.
\item The finiteness of the eigenvalues (in the spectral gap) of the perturbed Dirac operator is studied, under suitable decay assumptions on the potential perturbation. \end{itemize}
英文摘要：
Let
$$L_0=\suml_{j=1}^nM_j^0D_j+M_0^0,\,\,\,\,D_j=\frac{1}{i}\frac{\pa}{\paxj},
\quad x\in\Rn,$$
be a constant coefficient
first-order partial differential system, where the matrices $M_j^0$ are Hermitian. It is assumed that the homogeneous part is strongly propagative. In the nonhomegeneous case it is assumed that the operator is isotropic . The spectral theory of such systems and their potential perturbations is expounded, and a Limiting Absorption Principle is obtained up to thresholds. Special attention is given to a detailed study of the Dirac and Maxwell operators.
The estimates of the spectral derivative near the thresholds are based on detailed trace estimates on the slowness surfaces. Two applications of these estimates are presented:
\begin{itemize}
\item Global spacetime estimates of the associated evolution unitary groups, that are also commonly viewed as decay estimates. In particular the Dirac and Maxwell systems are explicitly treated.
\item The finiteness of the eigenvalues (in the spectral gap) of the perturbed Dirac operator is studied, under suitable decay assumptions on the potential perturbation. \end{itemize}
