Gibbs半群非自治扰动的解算子
Solution Operator for Non-Autonomous Perturbation of Gibbs Semigroup
摘要：
本文研究了可分希尔伯特空间上Gibbs半群的非自治扰动的线性动力学。证明了解非自治Cauchy问题的演化族{U（t，s）} 0 $\le$ s $\le$ t可以在迹范数拓扑中用乘积公式逼近.给出了乘积公式逼近式{Un（t，s）} {0 $\le$ s $\le$ t，$\ge$ 1}对解算子{U（t，s）} {0 $\le$ s $\le$ t}收敛速率.
英文摘要：
The paper is devoted to a linear dynamics for non-autonomous perturbation of the Gibbs semigroup on a separable Hilbert space. It is shown that evolution family {U(t, s)} 0$\le$s$\le$t solving the non-autonomous Cauchy problem can be approximated in the trace-norm topology by product formulae. The rate of convergence of product formulae approximants {U n (t, s)} {0$\le$s$\le$t,n$\ge$1} to the solution operator {U(t, s)} {0$\le$s$\le$t} is also established.
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