Related papers: An operator-theoretic approach to differential pos…
The existence and multiplicity of positive periodic solutions for first non-autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. The proof of our…
We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. By consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic…
We investigate the relationship between mapping cones and matrix ordered *-vector spaces (i.e., abstract operator systems). We show that to every mapping cone there is an associated operator system on the space of n-by-n complex matrices,…
In this work, we propose to apply the recently developed Koopman operator techniques to explore the global phase space of a nonlinear system from time-series data. In particular, we address the problem of identifying various invariant…
We identify a positivity property for partition functions in quantum systems with a unitary symmetry group, and we call this "twist positivity." The existence of Feynman-Kac measures and the existence of zero-mass limits are both related to…
We develop algorithms built around properties of the transfer operator and Koopman operator which 1) test for possible multiscale dynamics in a given dynamical system, 2) estimate the magnitude of the time-scale separation, and finally 3)…
This paper focuses on boundary approximate controllability under positivity constraints of a wide range of infinite-dimensional control systems. We develop frequency domain controllability criteria. Firstly, we derive a controllability…
We study Sturm-Liouville operators on closed sets of a special structure, which are sometimes referred as time scales and often appear in modelling various real processes. Depending on the set structure, such operators unify both…
In the present article, we propose the new class positive linear operators, which discrete type depending on a real parameters. These operators are similar to Jain operators but its approximation properties are different then Jain…
In this paper, we consider the systems with trajectories originating in the nonnegative orthant becoming nonnegative after some finite time transient. First we consider dynamical systems (i.e., fully observable systems with no inputs),…
Dynamic Mode Decomposition (DMD) is a popular data-driven analysis technique used to decompose complex, nonlinear systems into a set of modes, revealing underlying patterns and dynamics through spectral analysis. This review presents a…
Positive operator measures (with values in the space of bounded operators on a Hilbert space) and their generalizations, mainly positive sesquilinear form measures, are considered with the aim of providing a framework for their generalized…
In this paper, an extension to rules-based fault detection is demonstrated utilizing properties of the Koopman operator. The Koopman operator is an infinite-dimensional, linear operator that captures nonlinear, finite dimensional dynamics.…
Given a countable dense subset D of an infinite-dimensional separable Hilbert space H the set of operators for which every vector in D except zero is hypercyclic (weakly supercyclic) is residual for the strong (resp. weak) operator topology…
We develop a novel perspective on reflection positivity (RP) on the strip by systematically developing the analogies with the unit disc and the upper half plane in the complex plane. These domains correspond to the three conjugacy classes…
We define the associated geometric series for a large class of positive linear operators and study the convergence of the series in the case of sequences of admissible operators. We obtain an inverse Voronovskaya theorem and we apply our…
In this paper, we will show that a periodic nonlinear, time-varying dissipative system that is defined on a genus-p surface contains one or more invariant sets which act as attractors. Moreover, we shall generalize a result in [Martins,…
Inspired by some problems in Quantum Information Theory, we present some results concerning decompositions of positive operators acting on finite dimensional Hilbert spaces. We focus on decompositions by families having geometrical symmetry…
We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…
The Koopman operator framework provides a perspective that non-linear dynamics can be described through the lens of linear operators acting on function spaces. As the framework naturally yields linear embedding models, there have been…