Related papers: On Numerical Approximations of the Koopman Operato…
We study the dynamical properties of composition operators acting on Banach spaces of measurable functions. In particular, we study in some detail the composition operators induced by odometers, which allows us to give a variety of new…
Recent years have witnessed increasing interest to phase-amplitude reduction of limit-cycle dynamics. Adding an amplitude coordinate to the phase coordinate allows to take into account the dynamics transversal to the limit cycle and thereby…
Extended dynamic mode decomposition (EDMD) is a well-established method to generate a data-driven approximation of the Koopman operator for analysis and prediction of nonlinear dynamical systems. Recently, kernel EDMD (kEDMD) has gained…
This article contains the first steps in a general analysis of the problem of Krylov solvability of the inverse linear problem in a Banach space. In contrast to the well-studied Hilbert space setting, the Banach space setting presents…
This article investigates the convergence properties of s-numbers of certain truncations of bounded linear operators between Banach spaces. We prove a generalized version of a known convergence result for the approximation numbers of…
This work presents a comprehensive discretization theory for abstract linear operator equations in Banach spaces. The fundamental starting point of the theory is the idea of residual minimization in dual norms, and its inexact version using…
The present article deals with the local approximation results by means of Lipschitz maximal function, Ditzian-Totik modulus of smoothness and Lipschitz type space having two parameters for the summation-integral type operators defined by…
We obtain rates of convergence of numerical approximations of abstract linear parabolic evolution equations in Banach spaces. Our estimates extend known results from the literature of finite element approximations of parabolic equations to…
Koopmans spectral functionals aim to describe simultaneously ground state properties and charged excitations of atoms, molecules, nanostructures and periodic crystals. This is achieved by augmenting standard density functionals with simple…
We investigate the topological entropy of operators. More precisely, in the Banach space setting, we show that compact operators have finite entropy, which depends solely on their point spectrum. Moreover, for operators on \(F\)-spaces, we…
Residual Dynamic Mode Decomposition (ResDMD) offers a method for accurately computing the spectral properties of Koopman operators. It achieves this by calculating an infinite-dimensional residual from snapshot data, thus overcoming issues…
Dynamic mode decomposition (DMD) is a data-driven technique used for capturing the dynamics of complex systems. DMD has been connected to spectral analysis of the Koopman operator, and essentially extracts spatial-temporal modes of the…
The Carleman linearization is one of the mainstream approaches to lift a finite-dimensional nonlinear dynamical system into an infinite-dimensional linear system with the promise of providing accurate approximations of the original…
In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximal-projection method…
Koopman Mode Decomposition (KMD) is a technique of nonlinear time-series analysis that originates from point spectrum of the Koopman operator defined for an underlying nonlinear dynamical system. We present a numerical algorithm of KMD…
The eigenspectrum of the Koopman operator enables the decomposition of nonlinear dynamics into a sum of nonlinear functions of the state space with purely exponential and sinusoidal time dependence. For a limited number of dynamical…
We prove the applicability of the finite section method to an arbitrary operator in the Banach algebra generated by the operators of multiplication by piecewise continuous functions and the convolution operators with symbols in the algebra…
Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-including differential operators-are discontinuous or set-valued,…
This paper proposes Koopman operator-based Stochastic Model Predictive Control (K-SMPC) for enhanced lateral control of autonomous vehicles. The Koopman operator is a linear map representing the nonlinear dynamics in an infinite-dimensional…
We develop a novel EDMD-type algorithm that captures the spectrum of the Koopman operator defined on a reproducing kernel Hilbert space of analytic functions. This method, which we call analytic EDMD, relies on an orthogonal projection on…