区域上的人口算子的谱分析

本文讨论了区域上的人口算子谱的特性。证明了人口算子的谱由可数多个孤立的本征值组成,且关于实轴对称分布。存在且只存在一个具有实部最大特性的实本征值,且对应的本征函数是正函数。

THE SPECTRUM ANALYSIS OF POPULATION OPERATOR WITH DOMAIN

The spectrum property of population operator with domain is investigated. It is proved that the spectra of population operator with domain consist of numerable isolated eigenvalues, and range symmetrically about the axis, There exists only one real eigenvalue which has the real-maximal property. And the corresponding eigenfunction is positive.