具有四个状态可修复系统本征值分布

The Distribution of Eigenvalue with the Four-State Reparable System

给出一类具有四个状态可修复系统算子预解式特性,对任意给定的δ>0,r=a+bi,固定a1,a2,使得-μ+δ<a1≤a≤a2,得出lim b→∞‖R(r;A+E)‖=0,从而得到在r≥a1的右半平面内相应于系统算子A+E的谱点由有限个孤立特征值组成.

The property of operator＇s resoluent with the four-state reparable system is discussed. We randomly give δ 〉 0 and r = a ＋ bi. Let＇s fix a1 and a2, which is satisfying to -μ＋δ〈a1≤a≤a2. So, we get a conclusion is lim｜b｜→∞｜｜R（r;A＋E）｜｜=0. Consequently, we obtain that in the right plane of r ≥ a1 is composed of the finite isolating eigenvalue correspending spectrum of operator A ＋ E system.