In this talk we will present eigenvalue estimates for the solutions of operator Lyapunov equations with a noncompact (but relatively Hilbert Schmidt) control operator. We compute eigenvalue estimates from Galerkin discretizations of Lyapunov equations and discuss the appearance of spurious (non convergent) discrete eigenvalues. This phenomenon is called the spectral pollution. Our main tools,...
The Koopman linearization enables the use of the linear operator theory in the study of nonlinear dynamical systems by switching from a topological dynamical system $(K, \varphi)$ to a Koopman system $(C(K), T_{\varphi})$ consisting of the space $C(K)$ of continuous complex-valued functions on $K$ and the composition operator $T_{\varphi} \colon f \mapsto f \circ \varphi$ on $C(K).$
Let...
The concept of positive symmetric systems, also known as Friedrichs systems, originated with Kurt Otto Friedrichs in 1958. He demonstrated that this framework encompasses a broad range of initial and boundary value problems for various types of linear partial differential equations. Renewed interest in these systems emerged from advancements in the numerical analysis of differential equations,...
