相关论文: Internally Hankel $k$-positive systems
We introduce a new class of operators: ergodic families of self-adjoint Hankel operators realised as integral operators on the half-line. Inspired by the spectral theory of differential and finite-difference operators with ergodic…
For a finite reflection group on $\b R^N,$ the associated Dunkl operators are parametrized first-order differential-difference operators which generalize the usual partial derivatives. They generate a commutative algebra which is - under…
These lecture notes are intended as an introduction to the theory of rational Dunkl operators and the associated special functions, with an emphasis on positivity and asymptotics. We start with an outline of the general concepts: Dunkl…
This note is devoted to the intertwining operator in the one--dimensional trigonometric Dunkl setting. We obtain a simple integral expression of this operator and deduce its positivity.
In this paper, we study the problem of identifying the impulse response of a linear time invariant (LTI) dynamical system from the knowledge of the input signal and a finite set of noisy output observations. We adopt an approach based on…
We characterize the boundedness of a positive integral operator $T_K$, with kernel $K\in M_+(\R^{2n})$, between Lorentz-Gamma spaces $\Gamma_{p,\phi_2}(\R^n)$ and $\Gamma_{q,\phi_1}(\R^n)$, $1<p\le q<\infty$. The key step reduces the…
Large-scale linear, time-invariant (LTI) dynamical systems are widely used to characterize complicated physical phenomena. We propose a two-stage algorithm to reduce the order of a large-scale LTI system given samples of its transfer…
In this paper, we discuss the controllability of a family of linear time-invariant (LTI) networks defined on a signed graph. In this direction, we introduce the notion of positive and negative signed zero forcing sets for the…
An alternative formulation for the controllability problem of single input linear positive systems is presented. Driven by many industrial applications, this formulations focuses on the case where the region of interest is only a subset of…
We provide a simple construction of bipartite entangled states that are positive under partial transposition, and hence undistillable. The construction makes use of the properties of the projectors onto the symmetric and antisymmetric…
Positive systems play an important role in systems and control theory and have found many applications in multi-agent systems, neural networks, systems biology, and more. Positive systems map the nonnegative orthant to itself (and also the…
This paper presents a framework for inverse learning of objective functions for constrained optimal control problems, which is based on the Karush-Kuhn-Tucker (KKT) conditions. We discuss three variants corresponding to different model…
A new realist interpretation of quantum mechanics is introduced. Quantum systems are shown to have two kinds of properties: the usual ones described by values of quantum observables, which are called extrinsic, and those that can be…
This paper presents a tractable tube-based robust data-driven predictive control scheme that uses only a single finite noisy input-state trajectory of an unknown discrete-time linear time-invariant (LTI) system. A simplex constraint is…
A parameter-dependent class of Hamiltonian (generalized) Lotka-Volterra systems is considered. We prove that this class contains Liouville integrable as well as superintegrable cases according to particular choices of the parameters. We…
We consider a slowly decaying oscillatory potential such that the corresponding 1D Schr\"odinger operator has a positive eigenvalue embedded into the absolutely continuous spectrum. This potential does not fall into a known class of initial…
For a wide class of unbounded integral Hankel operators on the positive half-line, we prove essential self-adjointness on the set of smooth compactly supported functions.
Consider a binary classification problem in which the learner is given a labeled training set, an unlabeled test set, and is restricted to choosing exactly $k$ test points to output as positive predictions. Problems of this kind---{\it…
We present an alternative proof of the result by P. Gerard and S. Grellier, stating that given two real sequences $(\lambda_n)_{n=1}^\infty$, $(\mu_n)_{n=1}^\infty$ satisfying the intertwining relations \[ |\lambda_1| > |\mu_1| >…
The theory of linear time invariant systems is well established and allows, among other things, to formulate and solve control problems in finite time. In this context the control laws are typically taken in a space of the form L^p(0,T;U).…