{
  "abstract": "The study of regularity and solvability of partial differential operators on non-compact manifolds requires the construction of adapted functional spaces. In this work we introduce $\\mathcal{S}(\\mathfrak{M}\\times\\mathbb{R}^n)$, the Schwartz space on the product of a homogeneous space $\\mathfrak{M}$ and the Euclidean space $\\mathbb{R}^n$. We characterize $\\mathcal{S}(\\mathfrak{M}\\times\\mathbb{R}^n)$ and its topological dual by employing discrete Fourier analysis in terms of eigenfunction expansions associated with a class of anisotropic elliptic operators on $\\mathbb{R}^n$. We provide a characterization via partial Fourier coefficients and via full coefficients, that is, with respect to both components of $\\mathfrak{M} \\times \\mathbb{R}^n$ simultaneously, which is achieved by studying the Fourier analysis on $\\mathfrak{M}$. Our results provide new tools for the analysis of operators in this broader setting. As an application, we investigate the global existence and regularity of solutions for a class of partial differential equations on $\\mathfrak{M}\\times \\mathbb{R}^n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00302",
  "author_total": 3,
  "authors": [
    {
      "name": "Isadora Vieira Coelho da Silva"
    },
    {
      "name": "Paulo Leandro Dattori da Silva"
    },
    {
      "name": "Michael Ruzhansky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c9r9cmfems172.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00302",
  "fulltext_url": null,
  "id": "c9r9cmfems172",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00302",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00302",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c9r9cmfems172.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00302",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00302"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Fourier analysis on a class of Schwartz spaces and applications",
  "title_text": "Fourier analysis on a class of Schwartz spaces and applications",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/c9r9cmfems172",
  "venue": "arXiv",
  "versions": []
}