# Weak and Strong Approximation of Semigroups on Hilbert Spaces

@article{Chill2016WeakAS, title={Weak and Strong Approximation of Semigroups on Hilbert Spaces}, author={R. Chill and A. F. M. Elst}, journal={Integral Equations and Operator Theory}, year={2016}, volume={90}, pages={1-22} }

For a sequence of uniformly bounded, degenerate semigroups on a Hilbert space, we compare various types of convergences to a limit semigroup. Among others, we show that convergence of the semigroups, or of the resolvents of the generators, in the weak operator topology, in the strong operator topology or in certain integral norms are equivalent under certain natural assumptions which are frequently met in applications.

## 4 Citations

On homogenization of the first initial-boundary value problem for periodic hyperbolic systems

- Mathematics, PhysicsApplicable Analysis
- 2018

ABSTRACT Let be a bounded domain of class . In , we consider a self-adjoint matrix strongly elliptic second-order differential operator , , with the Dirichlet boundary condition. The coefficients of…

Feynman-Kac formula for perturbations of order $\leq 1$ and noncommutative geometry

- Physics, Mathematics
- 2020

Let Q be a differential operator of order ď 1 on a complex metric vector bundle E Ñ M with metric connection ∇ over a possibly noncompact Riemannian manifold M . Under very mild regularity…

On homogenization of periodic hyperbolic systems in $L_2(\mathbb{R}^d;\mathbb{C}^n)$. Variations on the theme of the Trotter-Kato theorem

- Mathematics
- 2019

In L2(R d;Cn), we consider a matrix elliptic second order differential operator Bε > 0. Coefficients of the operator Bε are periodic with respect to some lattice in Rd and depend on x/ε. We study the…

Variations on the theme of the Trotter-Kato theorem for homogenization of periodic hyperbolic systems

- Mathematics
- 2019

In $L_2(\mathbb{R}^d;\mathbb{C}^n)$, we consider a matrix elliptic second order differential operator $B_\varepsilon >0$. Coefficients of the operator $B_\varepsilon$ are periodic with respect to…

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