{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:0b8e66a2-7e78-4510-8c4c-61afabaae089",
  "labels": {
    "zh-CN": "傅里叶反演",
    "en": "Fourier inversion"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "f620e28cf6e35601fbf4347ec507097d38c2ba0fa0631a8ae1e069797f77a677",
  "occurrences": [
    {
      "concept_id": "urn:uuid:0b8e66a2-7e78-4510-8c4c-61afabaae089",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "zh-CN",
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-11/02-the-group-r-and-the-fourier-transform",
      "anchor": "first-da5867a3b26200f282bb-zh",
      "chapter": "11",
      "section": "11.2",
      "offset": 1565,
      "range": [
        8511,
        8849
      ],
      "source_revision": "001cc2dcd8b764bace6f211bd9e75d8d033ed36d4c29d64d3702dc5b08702d3d",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "theorem",
      "role_basis": {
        "kind": "registered-source-environment",
        "registered_position": {
          "route": "books/woit-qtgr/2025-10-20/zh/chapter-11/02-the-group-r-and-the-fourier-transform",
          "lang": "zh-CN",
          "section": "11.2",
          "signal": "named-theorem",
          "label": "傅里叶反演",
          "english": "",
          "offset": 1424
        }
      },
      "label": "> [!theorem] 定理（傅里叶反演）",
      "context": {
        "range": [
          8511,
          8849
        ],
        "quote": "\n\n> [!theorem] 定理（傅里叶反演）\n> 若 $\\psi\\in\\mathcal S(\\mathbf R)$，则 $\\widetilde\\psi\\in\\mathcal S(\\mathbf R)$，并且\n>\n> <span id=\"equation-11-4\" class=\"block-anchor\"></span>\n>\n> $$\n> \\psi (q) = \\widetilde {\\mathcal {F}} \\widetilde {\\psi} = \\frac {1}{\\sqrt {2 \\pi}} \\int_ {- \\infty} ^ {+ \\infty} e ^ {i k q} \\widetilde {\\psi} (k) d k\\tag{11.4}\n> $$\n",
        "quote_sha256": "ce12aa83cce2ab609a98ba788fc5e828a7cd74d46a184f0f666bd3c59c26315c",
        "environment": "theorem",
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-11/02-the-group-r-and-the-fourier-transform",
          "lang": "en",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-3962c9922197a31caee46c43"
    },
    {
      "concept_id": "urn:uuid:0b8e66a2-7e78-4510-8c4c-61afabaae089",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "en",
      "route": "books/woit-qtgr/2025-10-20/en/chapter-11/02-the-group-r-and-the-fourier-transform",
      "anchor": "first-44829821f911a73fa156-en",
      "chapter": "11",
      "section": "11.2",
      "offset": 3204,
      "range": [
        9310,
        9677
      ],
      "source_revision": "24b421910ee3d7532b1748c643b31ddf0f77d9ef4f396c4a63fdde48020bf3ef",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "theorem",
      "role_basis": {
        "kind": "registered-source-environment",
        "registered_position": {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-11/02-the-group-r-and-the-fourier-transform",
          "lang": "en",
          "section": "11.2",
          "signal": "named-theorem",
          "label": "Fourier inversion",
          "english": "Fourier inversion",
          "offset": 3063
        }
      },
      "label": "> [!theorem] Theorem (Fourier inversion)",
      "context": {
        "range": [
          9310,
          9677
        ],
        "quote": "\n\n> [!theorem] Theorem (Fourier inversion)\n> For $\\psi\\in\\mathcal S(\\mathbf R)$, one has $\\widetilde\\psi\\in\\mathcal S(\\mathbf R)$, and\n>\n> <span id=\"equation-11-4\" class=\"block-anchor\"></span>\n>\n> $$\n> \\psi (q) = \\widetilde {\\mathcal {F}} \\widetilde {\\psi} = \\frac {1}{\\sqrt {2 \\pi}} \\int_ {- \\infty} ^ {+ \\infty} e ^ {i k q} \\widetilde {\\psi} (k) d k\\tag{11.4}\n> $$\n",
        "quote_sha256": "576fa62694b9b2db3573cf9c55879824ae9a468861497e7cf93be4ce2106bec9",
        "environment": "theorem",
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/zh/chapter-11/02-the-group-r-and-the-fourier-transform",
          "lang": "zh-CN",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-6a0581100bb07257fbd63a54"
    }
  ],
  "registered_positions": [
    {
      "route": "books/woit-qtgr/2025-10-20/en/chapter-11/02-the-group-r-and-the-fourier-transform",
      "lang": "en",
      "section": "11.2",
      "signal": "named-theorem",
      "label": "Fourier inversion",
      "english": "Fourier inversion",
      "offset": 3063
    },
    {
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-11/02-the-group-r-and-the-fourier-transform",
      "lang": "zh-CN",
      "section": "11.2",
      "signal": "named-theorem",
      "label": "傅里叶反演",
      "english": "",
      "offset": 1424
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-3962c9922197a31caee46c43",
    "occ-6a0581100bb07257fbd63a54"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 2,
    "located_occurrences": 2,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "a12865a6555f9a03a15aa25cb7707d78a74f34994bb0d7ef6b9f0abc29a30aa0",
  "optional_enrichments": []
}