{
  "abstract": "A collection and clarification is given of the key mathematical details of the method of applying the convolution theorem as part of the solution to the two-dimensional magnetic inverse problem: reconstructing current density from magnetic field data. Particular emphasis is given to obtaining a closed-form solution for the Fourier transform of the convolution kernel that features in the Biot-Savart law. Having done this, the Fourier-transformed current density is obtained, via the convolution theorem, as a function of Fourier-transformed magnetic field data and other variables.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01862",
  "author_total": 1,
  "authors": [
    {
      "name": "Michael T. M. Woodley"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0gtnj53ra4rza.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01862",
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  "landing_url": "https://arxiv.org/abs/2609.01862",
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  "native_subjects": [
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      "arxiv",
      "math-ph"
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      "arxiv",
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      "2610|Numerical methods in inverse problems"
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  "pdf_url": "https://arxiv.org/pdf/2609.01862",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
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  "ris": "https://research.draconitic.com/paper/0gtnj53ra4rza.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2609.01862",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01862"
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  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Applying the convolution theorem to the two-dimensional magnetic inverse problem",
  "title_text": "Applying the convolution theorem to the two-dimensional magnetic inverse problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/0gtnj53ra4rza",
  "venue": "arXiv",
  "versions": []
}