Related papers: $L^p$ Boundedness of the Scattering Wave Operators…

For exponents $p,q\in (1,\infty),$ we study the $L^p$-to-$L^q$ boundedness and compactness of the commutator $[b,H_{\gamma}] = bH_{\gamma} - H_{\gamma}b,$ where $H_{\gamma}$ is the Hilbert transform along the monomial curve $\gamma$ and the…

For $N$-body Schr\"o\-dinger operators with time-periodic short-range pair-potentials we show by a time-dependent commutator method that all channel wave operators exist. For $N=2$ we prove asymptotic completeness by a simplified version of…

We give an explicit formula for the wave operators for Schroedinger operators on the half-line with a potential decaying strictly faster than the polynomial of degree minus two. The formula consists of the main term given by the scattering…

Making use of the weighted Mourre theory developed in [GJ1], we show the limiting absorption principle for Schr{\"o}dinger operators with perturbed oscillating potential on appropriate energy intervals. We focus on a certain class of…

We study multi-frequency quasiperiodic Schr\"{o}dinger operators on $\mathbb{Z} $. We prove that for a large real analytic potential satisfying certain restrictions the spectrum consists of a single interval. The result is a consequence of…

We prove uniform $L^p$ bounds for multilinear operators which are given by multipliers whose symbols are singular on a one dimensional subspace. The novelty is that these bounds are uniform in the choice of the subspace.

We consider scattering matrix for Schr\"odinger-type operators on $\mathbb{R}^d$ with perturbation $V(x)=O(\langle x\rangle^{-1})$ as $|x|\to\infty$. We show that the scattering matrix (with time-independent modifiers) is a…

Based on our previous study [IS3] on the stationary scattering theory for the Schrodinger operator on a manifold possessing an escape function we complete our investigation by doing the time-dependent counterpart. A particular class of…

We prove that the scattering operators and wave operators are well-defined in the energy space for the system of defocusing Schr\"odinger equations $$ \begin{cases} i\partial_t u_\mu + \Delta u_\mu - \sum_{\mu,\nu=1 }^N…

For an operator generating a group on $L^p$ spaces transference results give bounds on the Phillips functional calculus also known as spectral multiplier estimates. In this paper we consider specific group generators which are abstraction…

A one-dimensional scattering problem off a $\delta$-shaped potential is solved analytically and the time development of a wave packet is derived from the time-dependent Schr\"odinger equation. The exact and explicit expression of the…

Scattering states with LEED asymptotics are calculated for a general non-muffin tin potential, as e.g. for a pseudopotential with a suitable barrier and image potential part. The latter applies especially to the case of low lying conduction…

In this paper we investigate the spectral and the scattering theory of Schr\"odinger operators acting on perturbed periodic discrete graphs. The perturbations considered are of two types: either a multiplication operator by a short-range or…

Let $\alpha>0$, $H=(-\triangle)^{\alpha}+V(x)$, $V(x)$ belongs to the higher order Kato class $K_{2\alpha}(\mathbbm{R}^n)$. For $1\leq p\leq \infty$, we prove a polynomial upper bound of $\|e^{-itH}(H+M)^{-\beta}\|_{L^p, L^p}$ in terms of…

We study the theory of scattering for a class of Hartree type equations with long range interactions in arbitrary space dimension n > or = 1, including the case of Hartree equations with time dependent potential V(t,x) = kappa t^(mu -…

This paper can be considered as a sequel of [BS14] by Bernicot and Samoyeau, where the authors have proposed a general way of deriving Strichartz estimates for the Schr{\"o}dinger equation from a dispersive property of the wave propagator.…

We consider a scattering theory for convolution operators on $\mathcal{H}=\ell^2(\mathbb{Z}^d; \mathbb{C}^n)$ perturbed with a long-range potential $V:\mathbb{Z}^d\to\mathbb{R}^n$. One of the motivating examples is discrete Schr\"odinger…

We develop a unified approach to proving $L^p-L^q$ boundedness of spectral projectors, the resolvent of the Laplace-Beltrami operator and its derivative on $\mathbb{H}^d.$ In the case of spectral projectors, and when $p$ and $q$ are in…

We prove continuity properties of higher order commutators of fractional operators on the multilinear setting, between a product of weighted Lebesgue spaces into certain weighted Lipschitz spaces. The considered operators include the…

By means of appropriate sparse bounds, we deduce compactness on weighted $L^p(w)$ spaces, $1<p<\infty$, for all Calder\'on-Zygmund operators having compact extensions on $L^2(\mathbb{R}^n)$. Similar methods lead to new results on…