广义零程粒子系统预解算子的值域结构

研究了广义零程粒子系统生成元预解算子的映上性质及值域结构.作为粒子系统理论的主要研究对象之一的零程无穷粒子系统,描述了这样一种随机模型,在可列个位置上有无穷个不可辨粒子做随机的移动,同一时刻任何位置上最多只能发生一个粒子转移,粒子转移的概率转移速率仅受该位置的粒子数影响.将上述模型作了推广,研究了在同一时刻任一位置上可以发生任意有限个粒子转移的情形,使用了泛函分析的方法.研究表明:广义零程粒子系统的生成元预解算子具有映上性质且其值域恰好为其试验函数空间.

Range structure for the resolvent operator of the generator of a generalized infinite particle system with zero range interactions

This paper studies the onto mapping property and the range structure of the resolvent operator of an infinite particle system with zero range interactions.As a major research subject in particle system theory,the infinite particle system with zero range interactions describes a stochastic model with infinite unrecognized particles moving at random at countable sites.But at any time and at any site,there is only one single particle moving from one site to another.The probabilistic transition rate of particle is only related to the number of particles at the site.In the paper,we studied a more generalized situation where there are arbitrarily limited number of particles moving from one site to another at the same time.The functional analysis approach was employed to solve the problem.The range structure of the generator of a generalized infinite particle system with zero range interactions was given.The research result shows that,the resolvent operator of generalized infinite particle system with zero range interactions possesses onto mapping property,and its range is just the test function space.