{
  "abstract": "The notions of classical two-scale convergence and the periodic unfolding method, which both rely on an additional scale for the representation of periodic micro-oscillations, are in this paper traced back to the wider concept of general two-scale convergence. Moreover, a comparison is made between very weak two-scale convergence and periodic unfolding with respect to sequences bounded in Sobolev spaces, amplified by the scale of the micro-oscillations. It turns out that, for amplified sequences, these approaches are not equivalent in an immediate sense. The paper both serves as a literature overview, with examples and illustrations of the concepts of convergence, and contains new results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04478",
  "author_total": 6,
  "authors": [
    {
      "name": "Tatiana Danielsson"
    },
    {
      "name": "Liselott Flodén"
    },
    {
      "name": "Anders Holmbom"
    },
    {
      "name": "Pernilla Johnsen"
    },
    {
      "name": "Marianne Olsson Lindberg"
    },
    {
      "name": "Jens Persson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2mbrjra1x25jw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04478",
  "fulltext_url": null,
  "id": "2mbrjra1x25jw",
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  "landing_url": "https://arxiv.org/abs/2610.04478",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2613|Approximation Theory and Sequence Spaces"
    ]
  ],
  "openalex": "W3039077355",
  "pdf_url": "https://arxiv.org/pdf/2610.04478",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2mbrjra1x25jw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04478",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04478"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On some concepts of convergence and their connections",
  "title_text": "On some concepts of convergence and their connections",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/2mbrjra1x25jw",
  "venue": "arXiv",
  "versions": []
}