相关论文: Spectral inequalities for combinations of Hermite …

We provide new uncertainty principles for functions in a general class of Gelfand-Shilov spaces. These results apply, in particular, with the classical Gelfand-Shilov spaces as well as for spaces of functions with weighted Hermite…

Some recent works have shown that the heat equation posed on the whole Euclidean space is null-controllable in any positive time if and only if the control subset is a thick set. This necessary and sufficient condition for…

We establish a family of uncertainty principles for finite linear combinations of Hermite functions. More precisely, we give a geometric criterion on a subset $S\subset \RR^d$ ensuring that the $L^2$-seminorm associated to $S$ is equivalent…

In this paper, new spectral inequalities for finite combinations of eigenfunctions of anisotropic Shubin operators are presented. Given a subset $\omega$ and an energy level, we provide an explicit control of the ratio of the L 2 (R d)-norm…

We study the partial Gelfand-Shilov regularizing effect and the exponential decay for the solutions to evolution equations associated to a class of accretive non-selfadjoint quadratic operators, which fail to be globally hypoelliptic on the…

We consider the anisotropic Shubin operators $(-\Delta)^m + \vert x\vert^{2k}$ acting on the space $L^2(\mathbb R^n)$, with $k, m \geq1$ some positive integers. We provide sharp quantitative estimates in Gelfand-Shilov spaces for the…

We prove quantitative spectral inequalities for the (anisotropic) Shubin operators on the whole Euclidean space, thus relating for functions from spectral subspaces associated to finite energy intervals their $L^2$-norm on the whole space…

We investigate uncertainty relations for quantum observables evolving under non-Hermitian Hamiltonians, with particular emphasis on the role of metric operators. By constructing appropriate metrics in each dynamical regime, namely the…

We study an indefinite spectral problem for a second-order self-adjoint elliptic operator in an asymptotically thin cylinder. The operator coefficients and the spectral density function are assumed to be locally periodic in the axial…

We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let…

On a compact Riemannian manifold with boundary, we prove a spectral inequality for the bi-Laplace operator in the case of so-called "clamped" boundary conditions , that is, homogeneous Dirichlet and Neumann conditions simultaneously. We…

Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are…

In this paper, we discuss the approximate controllability for control systems governed by stochastic evolution hemivariational inequalities in Hilbert spaces. The interest in studying this type of equation comes from its application in some…

We study fractional hypoelliptic Ornstein-Uhlenbeck operators acting on $L^2(\mathbb{R}^n)$ satisfying the Kalman rank condition. We prove that the semigroups generated by these operators enjoy Gevrey regularizing effects. Two byproducts…

We extend a randomisation method, introduced by Shiffman-Zelditch and developed by Burq-Lebeau on compact manifolds for the Laplace operator, to the case of $\mathbb{R}^d$ with the harmonic oscillator. We construct measures, thanks to…

We prove that the thickness property is a necessary and sufficient geometric condition that ensures the (rapid) stabilization or the approximate null-controllability with uniform cost of a large class of evolution equations posed on the…

We study the exact null controllability of a class of non-autonomous conformable fractional semi-linear evolution systems with nonlocal initial conditions in Hilbert spaces. The analysis is carried out within the framework of conformable…

We survey recent results on the control problem for the heat equation on unbounded and large bounded domains. First we formulate new uncertainty relations, respectively spectral inequalities. Then we present an abstract control cost…

We obtain sharp convergence rates, using Dirichlet correctors, for solutions of wave equations in a bounded domain with rapidly oscillating periodic coefficients. The results are used to prove the exact boundary controllability that is…

We prove new bounds on the control cost for the abstract heat equation, assuming a spectral inequality or uncertainty relation for spectral projectors. In particular, we specify quantitatively how upper bounds on the control cost depend on…