Related papers: High frequency dispersive estimates for the Schrod…

We prove optimal (that is, without loss of derivatives) dispersive estimates for the Schrodinger group $e^{it(-\Delta+V)}$ for a class of real-valued potentials $V\in C^k(R^n)$ with $k>(n-3)/2$, where $n=4,5$.

We prove dispersive estimates for solutions to the Schrodinger equation with a real-valued potential $V\in L^\infty({\bf R}^n)$, $n\ge 4$, satisfying $V(x)=O(|x|^{-(n+2)/2-\epsilon})$, $|x|>1$, $\epsilon>0$.

We prove dispersive estimates at high frequency in dimension two for both the wave and the Schrodinger groupes for a very large class of real-valued potentials.

We prove dispersive estimates for the low frequency part of the Schrodinger group for a large class of potentials in dimensions greater or equal to four. As a consequence, we extend the result of Journe, Sofer and Sogge to a larger class of…

We prove optimal dispersive estimates for the wave group $e^{it\sqrt{-\Delta+V}}$ for a class of real-valued potentials $V\in C^{(n-3)/2}({\bf R}^n)$, $4\le n\le 7$, such that $\partial_x^\alpha V(x)=O(|x|^{-\delta})$ for $|x|>1$, where…

We prove a dispersive estimate for the evolution of Schroedinger operators H = -\Delta + V(x) in three dimensions. The potential should belong to the closure of bounded compactly-supported functions with respect to the golbal Kato norm.…

We prove dispersive estimates for solutions to the wave equation with a real-valued potential $V\in L^\infty({\bf R}^n)$, $n\ge 4$, satisfying $V(x)=O(|x|^{-(n+1)/2-\epsilon})$, $|x|>1$, $\epsilon>0$.

We prove dispersive bounds for fractional Schr\"odinger operators on $\mathbb R^n$ of the form $H=(-\Delta)^{\alpha}+V$ with $V$ a real-valued, decaying potential and $\alpha \notin\mathbb N$. We derive pointwise bounds on the resolvent…

We prove Strichartz estimates for the Schroedinger operator $H = -\Delta + V(t,x)$ with time-periodic complex potentials $V$ belonging to the scaling-critical space $L^{n/2}_x L^\infty_t$ in dimensions $n \ge 3$. This is done directly from…

We prove the dispersive and Strichartz estimates for solutions to the wave equation with a class of many-electric potentials in spatial dimension three. To obtain the desired dispersive estimate, based on the spectral properties of the…

We prove dispersive estimates at low frequency in dimensions n greater or equal to 4 for the wave equation for a very large class of real-valued potentials, provided the zero is neither an eigenvalue nor a resonance.

We prove a family of dispersive estimates for the higher order Schr\"odinger equation $iu_t=(-\Delta)^mu +Vu$ for $m\in \mathbb N$ with $m>1$ and $2m<n<4m$. Here $V$ is a real-valued potential belonging to the closure of $C_0$ functions…

We prove optimal high-frequency resolvent estimates for perturbations of the Laplacian by large long-range magnetic and electric potentials in all dimensions $n\ge 3$. As an application, we prove dispersive estimates for the corresponding…

In this paper, we consider the dispersive estimates for Schr\"odinger operators with Coulomb-like decaying potentials, such as $V(x)=-c|x|^{-\mu}$ for $|x|\gg 1$ with $0<\mu<2$, in one dimension. As an application, we establish both the…

We prove a dispersive estimate for the evolution of Schroedinger operators $H = -\Delta + V(x)$ in ${\mathbb R}^3$. The potential is allowed to be a complex-valued function belonging to $L^p(\R^3)\cap L^q(\R^3)$, $p < \frac32 < q$, so that…

We prove L^1 --> L^\infty estimates for linear Schroedinger equations in dimensions one and three. The potentials are only required to satisfy some mild decay assumptions. No regularity on the potentials is assumed.

We study the dispersive properties of the linear Schr\"odinger equation with a time-dependent potential $V(t,x)$. We show that an appropriate integrability condition in space and time on $V$, i.e. the boundedness of a suitable…

We consider the long time dynamics of nonlinear Schr\"odinger equations with an external potential. More precisely, we look at Hartree type equations in three or higher dimensions with small initial data. We prove an optimal decay estimate,…

We investigate $L^1(\mathbb R^n)\to L^\infty(\mathbb R^n)$ dispersive estimates for the Schr\"odinger operator $H=-\Delta+V$ when there is an eigenvalue at zero energy and $n\geq 5$ is odd. In particular, we show that if there is an…

We prove a dispersive estimate for the time-independent Schrodinger operator H = -\Delta + V in three dimensions. The potential V(x) is assumed to lie in the intersection L^p(R^3) \cap L^q(R^3), p < 3/2 < q, and also to satisfy a generic…