"abstract harmonic analysis" meaning in English

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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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        {
          "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": "quote"
        },
        {
          "ref": "2015, Gerald B. Folland, A Course in Abstract Harmonic Analysis, 2nd edition, Taylor & Francis (CRC Press):",
          "type": "quote"
        }
      ],
      "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"
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        [
          "harmonic analysis",
          "harmonic analysis"
        ],
        [
          "Fourier transform",
          "Fourier transform"
        ],
        [
          "function",
          "function"
        ],
        [
          "Hausdorff",
          "Hausdorff"
        ],
        [
          "locally compact",
          "locally compact"
        ],
        [
          "topological group",
          "topological group"
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      ],
      "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."
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        "uncountable"
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        "mathematics",
        "sciences",
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      "translations": [
        {
          "code": "it",
          "lang": "Italian",
          "sense": "branch of harmonic analysis",
          "tags": [
            "feminine"
          ],
          "word": "analisi armonica astratta"
        }
      ]
    }
  ],
  "word": "abstract harmonic analysis"
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  "lang_code": "en",
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        {
          "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": "quote"
        },
        {
          "ref": "2015, Gerald B. Folland, A Course in Abstract Harmonic Analysis, 2nd edition, Taylor & Francis (CRC Press):",
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        }
      ],
      "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"
        ],
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          "locally compact",
          "locally compact"
        ],
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          "topological group",
          "topological group"
        ]
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      "qualifier": "harmonic analysis; representation theory; harmonic analysis; representation theory",
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        "(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."
      ],
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  "translations": [
    {
      "code": "it",
      "lang": "Italian",
      "sense": "branch of harmonic analysis",
      "tags": [
        "feminine"
      ],
      "word": "analisi armonica astratta"
    }
  ],
  "word": "abstract harmonic analysis"
}