Dispersive estimates in ℝ3 with threshold eigenstates and resonances

Beceanu, Marius

doi:10.2140/apde.2016.9.813

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Dispersive estimates in $\mathbb{R}^3$ with threshold eigenstates and resonances

Marius Beceanu

Vol. 9 (2016), No. 4, 813–858

DOI: 10.2140/apde.2016.9.813

Abstract

We prove dispersive estimates in $ℝ^{3}$ for the Schrödinger evolution generated by the Hamiltonian $H = - Δ + V$ , under optimal decay conditions on $V$ , in the presence of zero-energy eigenstates and resonances.

Keywords

pointwise decay estimates, resonances, zero-energy eigenfunctions

Mathematical Subject Classification 2010

Primary: 35J10

Secondary: 47D08

Milestones

Received: 2 March 2015

Revised: 17 December 2015

Accepted: 26 February 2016

Published: 3 July 2016

Authors

Marius Beceanu
Institute for Advanced Study Einstein Drive Princeton, NJ 08540 United States

Vol. 9, No. 4, 2016