双连续α次积分C-半群的概率逼近问题

基于局部凸拓扑τ的Banach空间X上双连续α次积分C半群性质的研究,用概率论的方法,将算子半群理论和逼近论相结合,利用n次积分C半群收敛速度的概率型估计式、Rie-mann-Stieltjes积分、算子值数学期望、连续修正模的概念及双连续C半群的概率逼近,给出了双连续α次积分C半群的概率型逼近式及收敛速度的估计式。

Probabilistic approximations for bi-continuous α-times integrated C-semigroups

Based on the properties of the bi-continuous α-times integrated C-semigroups on Banach space X endowed with an additional locally convex topology τ,this paper features some brief probabilistic approximations and convergent rates by using the probability method,combining the theory of semigroups of linear operators with approximation theory,and depending on the probabilistic estimation of convergence rate for n-times integrated C-semigroups,Riemann-Stieltjes integral,operator-valued mathematical expect and continuous modified modulus and the probabilistic approximations of bi-continuous α-times integrated C-semigroups.