{
  "abstract": "For $d,n\\in\\mathbb{Z}_{\\geq1}$ and $p\\in[1,\\infty)\\setminus\\{2\\}$, we characterize all linear maps $s\\colon\\ell_d^p\\to\\ell_n^p$ for which there is $E\\subseteq X_d$ such that $\\|s(ξ)\\|_p=\\|ξ|_E\\|_p$ for every $ξ\\in\\ell_d^p$. We call these maps \\emph{restricted isometries}. Our Lamperti-type theorem gives a unique description of each such operator using a set transformation, a positive amplitude function, and a unimodular phase function. In particular, it includes noninjective and nonsurjective operators, even when the dimensions differ. We further characterize restricted isometries between finite $\\ell^p$-spaces with arbitrary positive atomic weights. Applications include formulas counting set transformations and uniform restricted isometries, as well as a geometric description of all restricted isometries with fixed column supports.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32615",
  "author_total": 5,
  "authors": [
    {
      "name": "Olivia Dalfollo-Daley"
    },
    {
      "name": "Alonso Delfín"
    },
    {
      "name": "Christina Fernández"
    },
    {
      "name": "Cameron Mars"
    },
    {
      "name": "Xintan Xia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/afk9589why9tg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32615",
  "fulltext_url": null,
  "id": "afk9589why9tg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32615",
  "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.FA"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7223687869",
  "pdf_url": "https://arxiv.org/pdf/2610.32615",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/afk9589why9tg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32615",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32615"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Restricted isometries in finite-dimensional $\\ell^p$-spaces",
  "title_text": "Restricted isometries in finite-dimensional ℓ^p-spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/afk9589why9tg",
  "venue": "arXiv",
  "versions": []
}