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PreprintarXiv licencearXiv

On some concepts of convergence and their connections

  • Tatiana Danielsson
  • Liselott Flodén
  • Anders Holmbom
  • Pernilla Johnsen
  • Marianne Olsson Lindberg
  • Jens Persson
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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.

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Cite

BibTeXRIS
BibTeX
@misc{danielsson2026some,
  title = {{On some concepts of convergence and their connections}},
  author = {Tatiana Danielsson and Liselott Flodén and Anders Holmbom and Pernilla Johnsen and Marianne Olsson Lindberg and Jens Persson},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04478},
  eprint = {2610.04478},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04478},
}
RIS
TY  - UNPB
TI  - On some concepts of convergence and their connections
AU  - Tatiana Danielsson
AU  - Liselott Flodén
AU  - Anders Holmbom
AU  - Pernilla Johnsen
AU  - Marianne Olsson Lindberg
AU  - Jens Persson
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2610.04478
UR  - https://arxiv.org/abs/2610.04478
AB  - 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.
ER  -