Related papers: Structure of wave operators in R^3

In this article we consider asymptotics for the spectral function of Schr\"odinger operators on the real line. Let $P:L^2(\mathbb{R})\to L^2(\mathbb{R})$ have the form $$ P:=-\tfrac{d^2}{dx^2}+W, $$ where $W$ is a self-adjoint first order…

In this work, we prove the existence of wave operator for the following generalized derivative nonlinear Schr\"odinger equation \begin{align*} i\partial_t u+\partial_x^2 u +i |u|^{2\sigma}\partial_x u=0, \end{align*} with…

We introduce a novel framework for the analysis of linear wave equations on nonstationary asymptotically flat spacetimes, under the assumptions of mode stability and absence of zero energy resonances for a stationary model operator. Our…

Finite rank perturbations of a semi-bounded self-adjoint operator A are studied in the scale of Hilbert spaces associated with A. A concept of quasi-boundary value space is used to describe self-adjoint operator realizations of regular and…

We extend several fundamental estimates regarding spectral multipliers for the free Laplacian on $\mathbb R^3$ to the case of perturbed Hamiltonians of the form $H=-\Delta+V$, where $V$ is a scalar real-valued potential. Results include…

For the scattering system given by the Laplacian in a half-space with a periodic boundary condition, we derive resolvent expansions at embedded thresholds, we prove the continuity of the scattering matrix, and we establish new formulas for…

We provide new formulae for the wave operators in the context of the Friedrichs-Faddeev model. Continuity with respect to the energy of the scattering matrix and a few results on eigenfunctions corresponding to embedded eigenvalues are also…

$V$ denotes arbitrary bounded bijection on Hilbert space $H$. We try to describe the sets of $V$-stable vectors, i.e. the set of elements $x$ of $H$ such that the sequence $\|V^N x\| (N=1,2,...)$ is bounded (we also consider some other…

We investigate $L^1(\mathbb R^4)\to L^\infty(\mathbb R^4)$ dispersive estimates for the Schr\"odinger operator $H=-\Delta+V$ when there are obstructions, a resonance or an eigenvalue, at zero energy. In particular, we show that if there is…

We illustrate the composition properties for an extended family of SG Fourier integral operators. We prove continuity results for operators in this class with respect to $L^2$ and weighted modulation spaces, and discuss continuity on…

A system of three quantum particles on the three-dimensional lattice $\Z^3$ with arbitrary "dispersion functions" having non-compact support and interacting via short-range pair potentials is considered. The energy operators of the systems…

In this paper we discuss applications of the geometric theory of composition operators on Sobolev spaces to the spectral theory of non-linear elliptic operators. The lower estimates of the first non-trivial Neumann eigenvalues of the…

We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend…

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 -…

In this work we consider the wave equation with a repulsive potential, either on the half line ${\mathbb R}^+$ or the Euclidean space ${\mathbb R}^d$ with $d\geq 3$. We combine the operator theory and the inward/outward energy theory to…

We prove the chaoticity and describe the spectral structure of Rolewicz-type weighted backward shift unbounded linear operators in the sequence spaces $l_p$ ($1\le p<\infty$) and $c_0$.

We consider the discrete Schr\"odinger operator $H=-\Delta+V$ with a sparse potential $V$ and find conditions guaranteeing either existence of wave operators for the pair $H$ and $H_0=-\Delta$, or presence of dense purely point spectrum of…

We prove that operators satisfying the hypotheses of the extrapolation theorem for Muckenhoupt weights are bounded on weighted Morrey spaces. As a consequence, we obtain at once a number of results that have been proved individually for…

Let $L=-\Delta+V$ be a Schr\"odinger operator acting on $L^2(\mathbb R^n)$, $n\ge1$, where $V\not\equiv 0$ is a nonnegative locally integrable function on $\mathbb R^n$. In this paper, we first define molecules for weighted Hardy spaces…

We consider the 3D Schr\"odinger operator $H = H_0 + V$ where $H_0 = (-i\nabla - A)^2$, $A$ is a magnetic potential generating a constant magnetic field of strength $b>0$, and $V$ is a short-range electric potential which decays…