{
  "abstract": "It is shown that if one knows \"sufficiently many\" snapshots (samples) from an individual solution of a Schrödinger-type equation-which is bandlimited in an appropriate sense-then the solution can be reconstructed by a simple formula similar to the Shannon formula for bandlimited signals. Furthermore, results demonstrate that by using snapshots of bandlimited solutions of a Schrödinger-type equation, one can reconstruct bandlimited solutions of some relevant diffusion- and wave-type equations. Interestingly, the reconstruction formulas are essentially independent of the operators defining the equations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21915",
  "author_total": 1,
  "authors": [
    {
      "name": "Isaac Z. Pesenson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/53pqxhtv9a4y6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21915",
  "fulltext_url": null,
  "id": "53pqxhtv9a4y6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21915",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7213907455",
  "pdf_url": "https://arxiv.org/pdf/2609.21915",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/53pqxhtv9a4y6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21915",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21915"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Reconstruction of solutions to abstract Schrodinger, diffusion, and wave-type equations from snapshots",
  "title_text": "Reconstruction of solutions to abstract Schrodinger, diffusion, and wave-type equations from snapshots",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/53pqxhtv9a4y6",
  "venue": "arXiv",
  "versions": []
}