由两个同型部件和一个修理设备组成的系统的主算子的谱

On the Spectrum of the Operator Corresponding to the System Consisting of Two Identical Units and a Repairman

文章研究了由两个同型部件和一个修理设备组成的系统的主算子在左半复平面中的谱.在一定的条件下,该系统的主算子在左半复平面中的任何带形区域至多有有限多个特征值,且这些特征值的几何重数为1.该模型的主算子的共轭算子在左半复平面中的任何带形区域至多有有限多个特征值,且这些特征值的几何重数为1.0是该系统的主算子及其共轭算子的严格占优特征值.

We study spectrum of the operator,which corresponds to the system consisting of two identical units and a repairman,on the left half complex plane and obtain that under a certain condition,the operator and its adjoint operator have finite eigenvalues with geometric multiplicity one in any strip region in the left half complex plane and 0 is a strictly dominant eigenvalue of the operator and its adjoint operator.