The $L^p$ boundedness of wave operators for the three-dimensional multi-centre point interaction

Abstract

We prove that, for arbitrary centres and strengths, the wave operators for three dimensional Schrödinger operators with multi-centre local point interactions are bounded in $L^p({\mathbb{R}}^3)$ for $1<p<3$ and unbounded otherwise.

arXiv commentto appear on Annales Henri Poincaré, 2017

References in corpus (4)

• L^p boundedness of the wave operator for the one dimensional Schroedinger operator
• Dispersive estimate for the Schroedinger equation with point interactions
• Wave operator bounds for 1-dimensional Schrödinger operators with singular potentials and applications
• Dispersive estimates for Schrödinger operators with point interactions in ${\mathbb{R}}^3$

Cited by in corpus (7)

• Two dimensional Schr{\" o}dinger operators with point interactions: threshold expansions, zero modes and $L^p$-boundedness of wave operators
• On the $L^p$ boundedness of wave operators for two-dimensional Schrödinger operators with threshold obstructions
• On the $L^p$ boundedness of the Wave Operators for fourth order Schrödinger operators
• Fractional powers and singular perturbations of quantum differential Hamiltonians
• A characterization of singular Schrödinger operators on the half-line
• Fractional Sobolev Spaces for the Singular-perturbed Laplace Operator in the $L^p$ setting
• Infinitesimal and Infinite Numbers as an Approach to Quantum Mechanics