{
  "abstract": "This paper investigates a necessary and sufficient condition for a measurable function on $\\mathbb{R}^{\\times} \\times \\mathbb{R}^{d}$ to be the continuous wavelet transform of a complex Radon measure on $\\mathbb{R}^{d}$ under suitable regularity conditions on the wavelets. We define a new norm on the collection of such functions and show that it is isometrically isomorphic to the Banach algebra of complex Radon measures under convolution. We show a wavelet inversion formula for measures, in a restricted sense. Under additional hypothesis, we provide a reconstruction formula for the measure of closed rectangles in $\\mathbb{R}^d$ using wavelet transforms. We have included supporting examples to substantiate these assumptions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29293",
  "author_total": 2,
  "authors": [
    {
      "name": "Tathagata Banerjee"
    },
    {
      "name": "Vaishakh Jayaprakash"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a37fpfteekdtz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29293",
  "fulltext_url": null,
  "id": "a37fpfteekdtz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29293",
  "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"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7223227691",
  "pdf_url": "https://arxiv.org/pdf/2610.29293",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a37fpfteekdtz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29293",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29293"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On Continuous Wavelet Transform of Complex Radon Measures on $\\mathbb{R}^{d}$",
  "title_text": "On Continuous Wavelet Transform of Complex Radon Measures on ℝ^d",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/a37fpfteekdtz",
  "venue": "arXiv",
  "versions": []
}