中科院数学与系统科学研究院
数学研究所
学术报告
分析讨论班
报告人：Valentin A. ZAGREBNOV（Institut de Mathematiques de Marseille）
题 目：About product formulae for non-autonomous Gibbs semigroups
时 间：2024.06.21（星期五）10:30-11:30 南楼N820
地 点：数学院南楼N820
摘 要：We study a linear evolution equation corresponding to small non-autonomous Holder continuous perturbations of the Gibbs semigroup on a separable Hilbert space. It is shown that strongly continuous evolution family {U(t,s)}0≤s≤t≤T which solves the non- autonomous Cauchy problem can be constructed for s < t as a limit in the trace-norm topology of the product approximants {Un (t,s)}{0≤s<t≤T} , n ≥ 1. We prove that estimates of the rate of convergence of these approximants to the trace-class solution operator {U(t,s)}{0≤s<t≤T} are related to estimates established for their rates of convergence in the operator-norm topology.
This result is partially based on the recent book:
Trotter-Kato Product Formulæ (Birkhauser-Springer 2024) by Valentin A.Zagrebnov, Hagen Neidhardt and Takashi Ichinose.
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