Year: 2017
Type: article
Abstract: Making use of the localised Putnam theory developed in [gj], we show the limiting absorption principle for Schrödinger operators with perturbed oscillating potential on appropriate energy intervals. We focus on a certain class of oscillating potentials (larger than the one in [GJ2]) that was already studied in [BD, DMR, DR1, DR2, MU, ReT1, ReT2]. Allowing long-range and short-range components and local singularities in the perturbation, we improve known results. A subclass of the considered potentials actually cannot be treated by the Mourre commutator method with the generator of dilations as conjugate operator. Inspired by [FH], we also show, in some cases, the absence of positive eigenvalues for our Schrödinger operators.
Source: Documenta Mathematica
DOI: 10.4171/dm/577
Authors: Thierry Jecko, Aiman Mbarek
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4295152429