{
  "abstract": "This article aims at bringing together some remarks, sometimes elementary, concerning the extension of the construction of biorthogonal families associated with parabolic control problems in any dimension with suitable estimates on the biorthogonal elements. Such construction is well-studied in the one dimensional case but pretty much open in other settings. The goal of this article is not to design such biorthogonal families but to prove that their existence with estimates allowing to solve moment problems is a necessary condition for null controllability to hold for a very large class of parabolic problems. Then, some characterizations of these biorthogonal families are given.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Morgan Morancey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4px3j94a4j1r2.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "4px3j94a4j1r2",
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  "landing_url": "https://hal.science/hal-05553829v2",
  "language": "en",
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
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      "hal",
      "1.math.math-oc"
    ]
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05553829/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4px3j94a4j1r2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:40Z",
      "native_id": "hal-05553829",
      "source": "hal",
      "url": "https://hal.science/hal-05553829v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-oc",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Some remarks on the moment method for null controllability of parabolic equations in any dimension",
  "title_text": "Some remarks on the moment method for null controllability of parabolic equations in any dimension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:40Z",
  "url": "https://research.draconitic.com/paper/4px3j94a4j1r2",
  "venue": "HAL",
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}