摘要
本文概述新近对于生灭过程和一维扩散过程在如下三个问题研究中所取得的若干代表性成果:四种情形的主特征值、等谱算子和离散谱;得到了在各种情形下主特征值统一的基本估计,其上、下界之比不超过4;给出了一维情形谱离散的简明判别准则.
This paper introduces shortly recent progress on the following three problems： The principal eigen- value in four cases, isospectral operators, and discrete spectrum, for birth-death processes and one-dimensional diffusion processes. Unified basic estimates of principal eigenvalues in various situations are obtained, the ratio of their upper and lower bounds is no more than 4. Short criteria for discrete spectrum are presented in dimension one,
出处
《中国科学：数学》
CSCD
北大核心
2015年第5期429-438,共10页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:11131003)资助项目
关键词
生灭过程
扩散过程
谱问题
birth-death process, diffusion process, spectral problem
