Limiting absorption principle for Schrödinger operators with oscillating potentials

zbMATH Open1370.35092arXiv1610.04369MaRDI QIDQ526159

Thierry Jecko, Aiman Mbarek

Publication date: 10 May 2017

Published in: Documenta Mathematica (Search for Journal in Brave)

Abstract: 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 oscillating potentials (larger than the one in [GJ2]) that was already studied in [BD, MU, ReT1, ReT2]. We allow long-range and short-range components and local singularities in the perturbation. We improve known results, the main novelty being the presence of a long-range perturbation. A subclass of the considered potentials actually cannot be treated by the usual Mourre commutator method. Inspired by [FH], we also show, in some cases, the absence of positive eigenvalues for our Schr{"o}dinger operators.

Full work available at URL: https://arxiv.org/abs/1610.04369

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zbMATH Keywords

Schrödinger operatorslimiting absorption principleoscillating potentials

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10)

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