{
  "abstract": "Making use of the weighted Mourre theory developed in [GJ1], 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, 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 Schrödinger operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "1610.04369",
  "author_total": 2,
  "authors": [
    {
      "name": "Thierry Jecko"
    },
    {
      "name": "Aiman Mbarek"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1wwe4syh1repx.bib",
  "cited_by": 6,
  "doi": "10.4171/dm/577",
  "fulltext_url": null,
  "id": "1wwe4syh1repx",
  "issns": [
    "1431-0643",
    "1431-0635"
  ],
  "landing_url": "https://hal.science/hal-01381212v3",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-ap"
    ],
    [
      "hal",
      "1.math.math-fa"
    ],
    [
      "hal",
      "1.math.math-mp"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W4295152429",
  "pdf_url": "https://hal.science/hal-01381212/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": "Universität Bielefeld",
  "ris": "https://research.draconitic.com/paper/1wwe4syh1repx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:02Z",
      "native_id": "hal-01381212",
      "source": "hal",
      "url": "https://hal.science/hal-01381212v3"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-mp",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "LIMITING ABSORPTION PRINCIPLE FOR SCHRÖDINGER OPERATORS WITH OSCILLATING POTENTIAL.",
  "title_text": "LIMITING ABSORPTION PRINCIPLE FOR SCHRÖDINGER OPERATORS WITH OSCILLATING POTENTIAL.",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:02Z",
  "url": "https://research.draconitic.com/paper/1wwe4syh1repx",
  "venue": "Documenta Mathematica",
  "versions": []
}