"Tauberian theorem" meaning in English

{
  "etymology_text": "After Austrian and Slovak mathematician Alfred Tauber (1866-1942).",
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  "lang_code": "en",
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      "coordinate_terms": [
        {
          "word": "Abelian theorem"
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      "examples": [
        {
          "ref": "1957, Einar Hille, Ralph Saul Phillips, Functional Analysis and Semi-groups, Part 1, American Mathematical Society, page 117",
          "text": "Paragraph five deals with (A*)-algebras and contains a proof of a vector-valued variant of Wiener's Tauberian theorem.",
          "type": "quotation"
        },
        {
          "text": "1988, Staff writer, Foreword, [1933, Norbert Wiener, The Fourier Integral and Certain of Its Applications], Cambridge University Press, 1988 reissue, page xi,\nNot only did the general Tauberian theorem give a unifying view on questions involving summations and limits, but it introduced a paradigm for what was called abstract harmonic analysis a few years later. […] Generalized harmonic analysis is the subject-matter of the last chapter, though it was conceived before the Tauberian theorems."
        },
        {
          "ref": "2000, Johann Boos, F. Peter Cass, Classical and Modern Methods in Summability, Oxford University Press, page 167",
          "text": "We should emphasize that our main concern is — besides the presentation of Tauberian theorems in the case of special summability methods — to put, by way of examples, different methods in the hands of the reader to prove Tauberian theorems in the case of special summability methods.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Any of a class of theorems which, for a given Abelian theorem, specifies conditions such that any series whose Abel sums converge (as stipulated by the Abelian theorem) is in fact convergent."
      ],
      "id": "en-Tauberian_theorem-en-noun-XM~sNyKl",
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          "Abelian theorem",
          "Abelian theorem"
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          "series",
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        [
          "Abel sum",
          "Abel sum"
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          "convergent",
          "convergent"
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      "raw_glosses": [
        "(mathematical analysis) Any of a class of theorems which, for a given Abelian theorem, specifies conditions such that any series whose Abel sums converge (as stipulated by the Abelian theorem) is in fact convergent."
      ],
      "synonyms": [
        {
          "word": "tauberian theorem"
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      ],
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        "mathematical-analysis",
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      "wikipedia": [
        "Abelian and tauberian theorems",
        "Alfred Tauber",
        "G. H. Hardy"
      ]
    }
  ],
  "word": "Tauberian theorem"
}

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  "coordinate_terms": [
    {
      "word": "Abelian theorem"
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  "etymology_text": "After Austrian and Slovak mathematician Alfred Tauber (1866-1942).",
  "forms": [
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        {
          "ref": "1957, Einar Hille, Ralph Saul Phillips, Functional Analysis and Semi-groups, Part 1, American Mathematical Society, page 117",
          "text": "Paragraph five deals with (A*)-algebras and contains a proof of a vector-valued variant of Wiener's Tauberian theorem.",
          "type": "quotation"
        },
        {
          "text": "1988, Staff writer, Foreword, [1933, Norbert Wiener, The Fourier Integral and Certain of Its Applications], Cambridge University Press, 1988 reissue, page xi,\nNot only did the general Tauberian theorem give a unifying view on questions involving summations and limits, but it introduced a paradigm for what was called abstract harmonic analysis a few years later. […] Generalized harmonic analysis is the subject-matter of the last chapter, though it was conceived before the Tauberian theorems."
        },
        {
          "ref": "2000, Johann Boos, F. Peter Cass, Classical and Modern Methods in Summability, Oxford University Press, page 167",
          "text": "We should emphasize that our main concern is — besides the presentation of Tauberian theorems in the case of special summability methods — to put, by way of examples, different methods in the hands of the reader to prove Tauberian theorems in the case of special summability methods.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Any of a class of theorems which, for a given Abelian theorem, specifies conditions such that any series whose Abel sums converge (as stipulated by the Abelian theorem) is in fact convergent."
      ],
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      "raw_glosses": [
        "(mathematical analysis) Any of a class of theorems which, for a given Abelian theorem, specifies conditions such that any series whose Abel sums converge (as stipulated by the Abelian theorem) is in fact convergent."
      ],
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        "Abelian and tauberian theorems",
        "Alfred Tauber",
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  "synonyms": [
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  "word": "Tauberian theorem"
}