Related papers: An operator theoretic approach to uniform (anti-)m…
Using five basic principles we treat Gerstenhaber/Lie brackets, BV operators and Master equations appearing in mathematical and physical contexts in a unified way. The different contexts for this are given by the different types of…
We consider Koopman operator theory in the context of nonlinear infinite-dimensional systems, where the operator is defined over a space of bounded continuous functionals. The properties of the Koopman semigroup are described and a…
Modeling the purposeful behavior of imperfect agents from a small number of observations is a challenging task. When restricted to the single-agent decision-theoretic setting, inverse optimal control techniques assume that observed behavior…
We develop a general theory of multilinear singular integrals with operator-valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the $\mathcal R$-boundedness condition…
Given an Archimedean order unit space (V,V^+,e), we construct a minimal operator system OMIN(V) and a maximal operator system OMAX(V), which are the analogues of the minimal and maximal operator spaces of a normed space. We develop some of…
In optimal control problems, there exist different kinds of extremals, that is, curves candidates to be solution: abnormal, normal and strictly abnormal. The key point for this classification is how those extremals depend on the cost…
As a class of L\'evy type Markov generators, nonlocal Waldenfels operators appear naturally in the context of investigating stochastic dynamics under L\'evy fluctuations and constructing Markov processes with boundary conditions (in…
Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying a special property must be prime. We present a "Prime Ideal Principle" that gives a uniform method of proving such facts, generalizing the…
In this paper the necessary conditions of optimality in the form of maximum principle are derived for a very general class of variational problems. This class includes problems with any optimization criteria and constraints that can be…
This paper derives some discrete maximum principles for $P1$-conforming finite element approximations for quasi-linear second order elliptic equations. The results are extensions of the classical maximum principles in the theory of partial…
We are concerned with the sign of the solutions of non-cooperative systems when the parameter varies near a principal eigenvalue of the system. With this aim we give precise estimates of the validity interval for the Antimaximum Principle…
Kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…
We introduce a unified framework for the construction of convolutions and product formulas associated with a general class of regular and singular Sturm-Liouville boundary value problems. Our approach is based on the application of the…
Von Neumann entropy (VNE) is a fundamental quantity in quantum information theory and has recently been adopted in machine learning as a spectral measure of diversity for kernel matrices and kernel covariance operators. While maximizing VNE…
Classical convergence theory of Runge-Kutta methods assumes that the time step is small relative to the Lipschitz constant of the ordinary differential equation (ODE). For stiff problems, that assumption is often violated, and a problematic…
Operator systems are the unital self-adjoint subspaces of the bounded operators on a Hilbert space. Complex operator systems are an important category containing the C*-algebras and von Neumann algebras, which is increasingly of interest in…
We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…
Classical matching theory can be defined in terms of matrices with nonnegative entries. The notion of Positive operator, central in Quantum Theory, is a natural generalization of matrices with nonnegative entries. Based on this point of…
The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak…