"abstract harmonic analysis" meaning in English

See abstract harmonic analysis in All languages combined, or Wiktionary

Noun

Head templates: {{en-noun|-}} abstract harmonic analysis (uncountable)
  1. (harmonic analysis, representation theory, topology) A branch of harmonic analysis dealing with generalised Fourier transforms that act on functions defined on Hausdorff locally compact topological groups. Tags: uncountable Categories (topical): Topology Translations (branch of harmonic analysis): analisi armonica astratta [feminine] (Italian)
    Sense id: en-abstract_harmonic_analysis-en-noun-TXjWZQ5T Categories (other): English entries with incorrect language header Topics: mathematics, sciences, topology

Download JSON data for abstract harmonic analysis meaning in English (2.4kB)

{
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "abstract harmonic analysis (uncountable)",
      "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": "topical",
          "langcode": "en",
          "name": "Topology",
          "orig": "en:Topology",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "1970, Edwin Hewitt, Kenneth A. Ross, Abstract Harmonic Analysis: Volume II: Structure and Analysis for Compact Groups; Analysis on Locally Compact Abelian Groups, Springer, 2nd reprint, 2002, page 547,\nWIENER [1] goes well beyond analysis of periodic functions on R or even functions in 𝔏₂(R); this important paper has yet to be interpreted and assimilated into the standard repertory of abstract harmonic analysis."
        },
        {
          "ref": "2014, Anton Deitmar, Siegfried Echterhoff, Principles of Harmonic Analysis, 2nd edition, Springer, page v",
          "text": "The present book is a text book for a graduate course on abstract harmonic analysis and its applications.",
          "type": "quotation"
        },
        {
          "text": "2015, Gerald B. Folland, A Course in Abstract Harmonic Analysis, 2nd edition, Taylor & Francis (CRC Press):",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A branch of harmonic analysis dealing with generalised Fourier transforms that act on functions defined on Hausdorff locally compact topological groups."
      ],
      "id": "en-abstract_harmonic_analysis-en-noun-TXjWZQ5T",
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "harmonic analysis",
          "harmonic analysis"
        ],
        [
          "Fourier transform",
          "Fourier transform"
        ],
        [
          "function",
          "function"
        ],
        [
          "Hausdorff",
          "Hausdorff"
        ],
        [
          "locally compact",
          "locally compact"
        ],
        [
          "topological group",
          "topological group"
        ]
      ],
      "qualifier": "harmonic analysis; representation theory; harmonic analysis; representation theory",
      "raw_glosses": [
        "(harmonic analysis, representation theory, topology) A branch of harmonic analysis dealing with generalised Fourier transforms that act on functions defined on Hausdorff locally compact topological groups."
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ],
      "translations": [
        {
          "code": "it",
          "lang": "Italian",
          "sense": "branch of harmonic analysis",
          "tags": [
            "feminine"
          ],
          "word": "analisi armonica astratta"
        }
      ]
    }
  ],
  "word": "abstract harmonic analysis"
}
{
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "abstract harmonic analysis (uncountable)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "English uncountable nouns",
        "Quotation templates to be cleaned",
        "en:Topology"
      ],
      "examples": [
        {
          "text": "1970, Edwin Hewitt, Kenneth A. Ross, Abstract Harmonic Analysis: Volume II: Structure and Analysis for Compact Groups; Analysis on Locally Compact Abelian Groups, Springer, 2nd reprint, 2002, page 547,\nWIENER [1] goes well beyond analysis of periodic functions on R or even functions in 𝔏₂(R); this important paper has yet to be interpreted and assimilated into the standard repertory of abstract harmonic analysis."
        },
        {
          "ref": "2014, Anton Deitmar, Siegfried Echterhoff, Principles of Harmonic Analysis, 2nd edition, Springer, page v",
          "text": "The present book is a text book for a graduate course on abstract harmonic analysis and its applications.",
          "type": "quotation"
        },
        {
          "text": "2015, Gerald B. Folland, A Course in Abstract Harmonic Analysis, 2nd edition, Taylor & Francis (CRC Press):",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A branch of harmonic analysis dealing with generalised Fourier transforms that act on functions defined on Hausdorff locally compact topological groups."
      ],
      "links": [
        [
          "topology",
          "topology"
        ],
        [
          "harmonic analysis",
          "harmonic analysis"
        ],
        [
          "Fourier transform",
          "Fourier transform"
        ],
        [
          "function",
          "function"
        ],
        [
          "Hausdorff",
          "Hausdorff"
        ],
        [
          "locally compact",
          "locally compact"
        ],
        [
          "topological group",
          "topological group"
        ]
      ],
      "qualifier": "harmonic analysis; representation theory; harmonic analysis; representation theory",
      "raw_glosses": [
        "(harmonic analysis, representation theory, topology) A branch of harmonic analysis dealing with generalised Fourier transforms that act on functions defined on Hausdorff locally compact topological groups."
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "mathematics",
        "sciences",
        "topology"
      ]
    }
  ],
  "translations": [
    {
      "code": "it",
      "lang": "Italian",
      "sense": "branch of harmonic analysis",
      "tags": [
        "feminine"
      ],
      "word": "analisi armonica astratta"
    }
  ],
  "word": "abstract harmonic analysis"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-04-26 from the enwiktionary dump dated 2024-04-21 using wiktextract (93a6c53 and 21a9316). 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.