Let $H_0$ be a purely absolutely continuous selfadjoint operator acting on some separable infinite-dimensional Hilbert space and V be a compact perturbation. We relate the regularity properties of V to various spectral properties of the perturbed operator $H_0+V$. The structures of the discrete spectrum and the embedded eigenvalues are analyzed jointly with the existence of limiting absorption principles in a unified framework. Our results are based on a suitable combination of complex scaling techniques, resonance theory and positive commutators methods. Various results scattered throughout the literature are recovered and extended. For illustrative purposes, the case of the one-dimensional discrete Laplacian is emphasized.

让 $H_0$是一个作用于可分离的无限维希尔伯特空间上的纯绝对连续自伴算子，V是一个紧凑的扰动。我们将V的正则性质与扰动算子的各种光谱性质相关联$H_0+V$。在一个统一的框架下，结合极限吸收原理的存在，对离散光谱的结构和嵌入的特征值进行了分析。我们的结果基于复杂的缩放技术，共振理论和正换向器方法的适当组合。恢复并扩展了散布在整个文献中的各种结果。为了说明的目的，强调了一维离散拉普拉斯算子的情况。