Семинар Добрушинской лаборатории

Когда: вторник 17 июня, 16:15
Где: Адм. корпус, ауд.322.

Доклад:

Valentin Zagrebnov (Universty Aix-Marseille),
"What do we actually know about the operator-norm convergent Trotter-Kato product formula?"

Since 1875 due to Sophus Lie it is known that for any pair of (noncommutative) finite square matrices A and B as generators one has the norm estimate O(1/n) for convergence rate of the exponential product formula. In 1959 H.Trotter proved this formula in the strong operator topology on the Banach space for strongly continuous semigroups and unbounded generators A and B. Further, in 1978 T.Kato extended this result (still in the strong operator topology) to the non-exponential product formulae.

A breakthrough result in this direction was presented in the Dzh.L.Rogava theorem (1993). It says that on a separable Hilbert space the exponential Trotter product formula may converge in the operator-norm topology with convergence rate of the order O(ln(n)/sqrt(n)). This discovery initiated a number of papers addressed to the study of conditions on generators A and B aiming to optimise the rate of convergence in Rogava’s assertion.

Motivated by this discovery the optimal rate of convergence O(1/n) in the operator-norm topology under conditions of the Rogava theorem was proved only in 2001 (the Ichinose-Tamura-Tamura-Zagrebnov theorem) for both the Trotter and the Trotter-Kato product formulae. Under new fractional conditions on generators A and B the optimal rate of the Trotter-Kato product formulae convergence in the operator-norm topology on a Hilbert space was established in the Ichinose-Neidhardt-Zagrebnov (INZ)-theorem (2004).

I shall present these and some other recent results about the Lie-Trotter-Kato product formulae on Hilbert and Banach spaces, which are collected in the book: V.A.Zagrebnov, H.Neidhardt, T.Ichinose, Trotter-Kato Product Formulae, 2024.


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Страницы семинара:
https://sites.google.com/view/dobr-seminar
https://www.mathnet.ru/conf167

Адрес: МФТИ, Административный корпус, ауд. 322,
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