Related papers: Dispersive Estimates for Manifolds with one Trappe…

We show that for a one-dimensional Schr\"odinger operator with a potential whose first moment is integrable the scattering matrix is in the unital Wiener algebra of functions with integrable Fourier transforms. Then we use this to derive…

In this paper, we adapt the well-known \emph{local} uniqueness results of Borg-Marchenko type in the inverse problems for one dimensional Schr{\"o}dinger equation to prove \emph{local} uniqueness results in the setting of inverse…

We prove global Strichartz estimates (with spectral cutoff on the low frequencies) for non trapping metric perturbations of the Schroedinger equation, posed on the Euclidean space.

Our aim in this work is to give some quantitative insight on the dispersive effects exhibited by solutions of a semiclassical Schr{\"o}dinger-type equation in R d. We describe quantitatively the localisation of the energy in a long-time…

In this note we consider the Schr\"odinger equation on compact manifolds equipped with possibly degenerate metrics. We prove Strichartz estimates with a loss of derivatives. The rate of loss of derivatives depends on the degeneracy of…

We establish global bounds for solutions to stationary and time-dependent Schr\"odinger equations associated with the sublaplacian $\mathcal L$ on the Heisenberg group, as well as its pure fractional power $\mathcal L^s$ and conformally…

We consider the uniform resolvent and orthonormal Strichartz estimates for the Schr\"odinger operator. First we prove the Keel-Tao type theorem for the orthonormal Strichartz estimates, which means that the dispersive estimates yield the…

Let $(M,g)$ be a compact smooth $3$-dimensional Riemannian manifold without boundary. It is proved that the energy-critical nonlinear Schr\"odinger equation is globally well-posed for small initial data in $H^1(M)$, provided that a certain…

We establish dispersive estimates and local decay estimates for the time evolution of non-self-adjoint matrix Schr\"odinger operators with threshold resonances in one space dimension. In particular, we show that the decay rates in the…

We study the fourth order Schr\"odinger equation with mixed dispersion on an $N$-dimensional Cartan-Hadamard manifold. At first, we focus on the case of the hyperbolic space. Using the fact that there exists a Fourier transform on this…

The purpose of this note is to present an alternative proof of a result by H. Smith and C. Sogge showing that in odd dimension of space, local (in time) Strichartz estimates and exponential decay of the local energy for solutions to wave…

We prove global smoothing and Strichartz estimates for the Schroedinger, wave, Klein-Gordon equations and for the massless and massive Dirac systems, perturbed with singular electromagnetic potentials. We impose a smallness condition on the…

The possibility of finite-time, dispersive blow up for nonlinear equations of Schroedinger type is revisited. This mathematical phenomena is one of the possible explanations for oceanic and optical rogue waves. In dimension one, the…

We derive a dispersion estimate for one-dimensional perturbed radial Schr\"odinger operators. We also derive several new estimates for solutions of the underlying differential equation and investigate the behavior of the Jost function near…

In this paper, we prove the decay and scattering in the energy space for nonlinear Schr\"odinger equations with regular potentials in $\Bbb R^d$ namely, $i{\partial _t}u + \Delta u - V(x)u + \lambda |u|^{p - 1}u = 0$. We will prove decay…

We investigate quantitative (or effective) versions of the limiting absorption principle, for the Schr\"odinger operator on asymptotically conic manifolds with short-range potentials, and in particular consider estimates of the form $$ \|…

We obtain improved Strichartz estimates for solutions of the Schr\"odinger equation on negatively curved compact manifolds which improve the classical universal results results of Burq, G\'erard and Tzvetkov [11] in this geometry. In the…

We prove a dispersive estimate for the one-dimensional Schroedinger equation, mapping between weighted $L^p$ spaces with stronger time-decay ($t^{-3/2}$ versus $t^{-1/2}$) than is possible on unweighted spaces. To satisfy this bound, the…

We consider the Schroedinger operator in R^3 with N point interactions placed at Y=(y_1, ... ,y_N), y_j in R^3, of strength a=(a_1, ... ,a_N). Exploiting the spectral theorem and the rather explicit expression for the resolvent we prove a…

For compact, isometrically embedded Riemannian manifolds $ N \hookrightarrow \mathbb{R}^L$, we introduce a fourth-order version of the wave map equation. By energy estimates, we prove an $\textit{a priori}$ estimate for smooth local…