Related papers: Unique continuation and Hardy's uncertainty princi…
In this paper, we study the uncertainty principle for Schr\"odinger equations with a bounded time-independent potentials on certain Cartan-Hadamard manifolds endowed with an asymptotic hyperbolic metric in dimensions $n\geq2$. The classical…
We prove a logarithmic convexity result for exponentially weighted $L^2$-norms of solutions to electromagnetic Schr\"odinger equation, without needing to assume smallness of the magnetic potential. As a consequence, we can prove a unique…
In this paper, we study Hardy-type uncertainty principles and unique continuation properties for linear covariant Schrodinger equations with variable coefficients in the presence of bounded electric and magnetic potentials. Under suitable…
We prove unique continuation properties for linear variable coefficient Schr\"odinger equations with bounded real potentials. Under certain smallness conditions on the leading coefficients, we prove that solutions decaying faster than any…
We give a new proof of Hardy's uncertainty principle, up to the end-point case, which is only based on calculus. The method allows us to extend Hardy's uncertainty principle to Schr\"odinger equations with non-constant coefficients. We also…
In this paper we investigate the Cauchy problem for Schr\"odinger ultrahyperbolic equations with singular (less than continuous) coefficients. We prove $H^\infty$ well-posedness in the very weak sense under suitable assumptions of the…
We prove a sharp version of the Hardy uncertainty principle for Schr\"odinger equations with external bounded electromagnetic potentials, based on logarithmic convexity properties of Schr\"odinger evolutions. We provide, in addition, an…
We prove the logarithmic convexity of certain quantities, which measure the quadratic exponential decay at infinity and within two characteristic hyperplanes of solutions of Schr\"odinger evolutions. As a consequence we obtain some…
We study uniqueness properties of solutions of Schr\"odinger equations. The aim is to obtain sufficient conditions on the decay behavior of the difference of two solution $u_1-u_2$ of the equation at two different times $t_0=0$ and $t_1=1$…
In this paper, Hardy's uncertainty principle and unique continuation properties of abstract Schr\"odinger equations in vector-valued classes are obtained
In this paper, we investigate properties of unique continuation for hyperbolic Schr\"odinger equations with time-dependent complex-valued electric fields and time-independent real magnetic fields. We show that positive masses inside of a…
In this paper, we prove the strong unique continuation property at the origin for solutions of the following scaling critical parabolic differential inequality \[ |\operatorname{div} (A(x,t) \nabla u) - u_t| \leq \frac{M}{|x|^{2}} |u|,\ \ \…
We prove that if a solution of the discrete time-dependent Schr\"odinger equation with bounded real potential decays fast at two distinct times then the solution is trivial. For the free Shr\"odinger operator and for operators with…
Hardy's uncertainty principle is a classical result in harmonic analysis, stating that a function in $L^2(\mathbb{R}^d)$ and its Fourier transform cannot both decay arbitrarily fast at infinity. In this paper, we extend this principle to…
In this paper, Hardy's uncertainty principle and unique continuation properties of Schrodinger equations with operator potentials in Hilbert space-valued classes are obtained. Since the Hilbert space H and linear operators are arbitrary, by…
In this paper, we derive a local unique continuation property for stochastic hyperbolic equations without boundary conditions. This result is proved by a global Carleman estimate.
Asymptotics of solutions to relativistic fractional elliptic equations with Hardy type potentials is established in this paper. As a consequence, unique continuation properties are obtained.
We give a new proof of the $L^2$ version of Hardy's uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new log-convexity properties and the derivation of optimal Gaussian decay…
In this note we prove the strong unique continuation property at the origin for the solutions of the parabolic differential inequality \[ |\Delta u - u_t| \leq \frac{M}{|x|^2} |u|, \] with the critical inverse square potential. Our main…
In this paper, we establish a Paley-Wiener type uncertainty principle for Schr\"odinger equations with bounded electric and magnetic potentials, \begin{align*} i\partial_tu+\Delta_Au+V(t,x)u=0,\,\,u(0,x)=u_0(x), \end{align*} where…