Related papers: Observability inequalities on measurable sets for …
In this paper, we present a collection of results on the observability of quantum mechanical systems, in the case the output is the result of a discrete nonselective measurement. By defining an effective observable we extend previous…
In this article we study some problems related to the incompressible 3D Navier-Stokes equations from the point of view of Lebesgue spaces of variable exponent. These functional spaces present some particularities that make them quite…
The Clauser-Horne-Shimony and Holt inequality applies when measurements with binary outcomes are performed on physical systems under the assumption of local realism. Testing such inequalities in the quantum realm usually involves either…
This paper presents two general criteria to determine spaceability results in the complements of unions of subspaces. The first criterion applies to countable unions of subspaces under specific conditions and is closely related to the…
We establish functional analytic properties of the Stokes operator with bounded measurable coefficients on $L^p_{\sigma} (\mathbb{R}^d)$, $d \geq 2$, for $\lvert 1 / p - 1 / 2 \rvert < 1 / d$. These include optimal resolvent bounds and the…
We study various optimality criteria for quantum observables. Observables are represented as covariant positive operator valued measures and we consider the case when the symmetry group is compact. Phase observables are examined as an…
This paper considers the relevance of the concepts of observability and computability in physical theory. Observability is related to verifiability which is essential for effective computing and as physical systems are computational systems…
In the first part of this Chapter, we discuss the role of spectral observables, describing possible ways to build them from discretizations of the Laplace--Beltrami operator on triangulations, and how to extract useful geometric…
The existence of incompatibility is one of the most fundamental features of quantum theory, and can be found at the core of many of the theory's distinguishing features, such as Bell inequality violations and the no-broadcasting theorem. A…
We give an optimal in mixed (anisotropic) Strichartz type Lebesgue space-time norm estimates for the solution of linear parabolic inhomogeneous initial problem, with are exact or exact up to multiplicative constant coefficient evaluation.
In this short article we show a particular version of the Hedberg inequality which can be used to derive, in a very simple manner, functional inequalities involving Sobolev and Besov spaces in the general setting of Lebesgue spaces of…
The purpose of this note is to use the results and methods of our previous work with Bourgain to obtain control and observability by rough functions and sets on rectangular 2-tori. We show that any Lebesgue measurable set of positive…
We focus on the log-Sobolev inequality for spin systems on the lattice with interactions of higher order than quadratic. We show that if the one-dimensional single-site measure with boundaries satisfies the log-Sobolev inequality uniformly…
While the design of optimal peak-to-peak controllers/observers for linear systems is known to be a difficult problem, this problem becomes interestingly much easier in the context of interval observers because of the positive nature of the…
The ability of new instruments for providing accurate inferences of vector magnetic fields and line-of-sight velocities of the solar plasma depends a great deal on the sensitivity to these physical quantities of the spectral lines chosen to…
We analyse stability of observability estimates for solutions to wave and Scr\" odinger equations subjected to additive perturbations. The paper generalises the recent averaged observability/control result by allowing for systems consisting…
A limitation on simultaneous measurement of two arbitrary positive operator valued measures is discussed. In general, simultaneous measurement of two noncommutative observables is only approximately possible. Following Werner's formulation,…
For continuous maps on a compact manifold M, particularly for those that do not preserve the Lebesgue measure m, we define the observable invariant probability measures as a generalization of the physical measures. We prove that any…
This work proposes a detectability condition for linear time-varying systems based on the exponential dichotomy spectrum. The condition guarantees the existence of an observer, whose gain is determined only by the unstable modes of the…
We provide an observability inequality in terms of a measurable set for general Gevrey regular functions. As an application, we establish an observability estimate from a measurable set for sums of Laplace eigenfunctions in a compact and…