"Riemann-Lebesgue lemma" meaning in English

See Riemann-Lebesgue lemma in All languages combined, or Wiktionary

Noun

Etymology: Named after Bernhard Riemann and Henri Lebesgue. Head templates: {{en-noun|?}} Riemann-Lebesgue lemma
  1. (mathematics) A lemma, of importance in harmonic analysis and asymptotic analysis, stating that the Fourier transform or Laplace transform of an L1 function vanishes at infinity. Categories (topical): Mathematics

Download JSON data for Riemann-Lebesgue lemma meaning in English (1.6kB)

{
  "etymology_text": "Named after Bernhard Riemann and Henri Lebesgue.",
  "head_templates": [
    {
      "args": {
        "1": "?"
      },
      "expansion": "Riemann-Lebesgue lemma",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A lemma, of importance in harmonic analysis and asymptotic analysis, stating that the Fourier transform or Laplace transform of an L1 function vanishes at infinity."
      ],
      "id": "en-Riemann-Lebesgue_lemma-en-noun-4tj2dl7q",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "lemma",
          "lemma"
        ],
        [
          "Fourier transform",
          "Fourier transform"
        ],
        [
          "Laplace transform",
          "Laplace transform"
        ],
        [
          "vanish",
          "vanish"
        ],
        [
          "infinity",
          "infinity"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A lemma, of importance in harmonic analysis and asymptotic analysis, stating that the Fourier transform or Laplace transform of an L1 function vanishes at infinity."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "Riemann-Lebesgue lemma"
}
{
  "etymology_text": "Named after Bernhard Riemann and Henri Lebesgue.",
  "head_templates": [
    {
      "args": {
        "1": "?"
      },
      "expansion": "Riemann-Lebesgue lemma",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English entries with language name categories using raw markup",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English nouns with unknown or uncertain plurals",
        "English terms with non-redundant non-automated sortkeys",
        "en:Mathematics"
      ],
      "glosses": [
        "A lemma, of importance in harmonic analysis and asymptotic analysis, stating that the Fourier transform or Laplace transform of an L1 function vanishes at infinity."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "lemma",
          "lemma"
        ],
        [
          "Fourier transform",
          "Fourier transform"
        ],
        [
          "Laplace transform",
          "Laplace transform"
        ],
        [
          "vanish",
          "vanish"
        ],
        [
          "infinity",
          "infinity"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A lemma, of importance in harmonic analysis and asymptotic analysis, stating that the Fourier transform or Laplace transform of an L1 function vanishes at infinity."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "Riemann-Lebesgue lemma"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-20 from the enwiktionary dump dated 2024-05-02 using wiktextract (1d5a7d1 and 304864d). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.