"differential operator" meaning in English

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  "pos": "noun",
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      "examples": [
        {
          "text": "Define P(D) to be the differential operator given by P(D)#x3D;D²#x2B;5D#x2B;6, where D is the differentiation operator. Then P(D)(#x5C;sin(x))#x3D;-#x5C;sin(x)#x2B;5#x5C;cos(x)#x2B;6.",
          "type": "example"
        },
        {
          "ref": "2000, S. Albeverio, P. Kurasov, Singular Perturbations of Differential Operators, page 328",
          "text": "[…]these conditions appeared in the very first papers on ordinary differential operators.",
          "type": "quotation"
        },
        {
          "ref": "2012, Youri Egorov, Bert-Wolfgang Schulze, Pseudo-Differential Operators, Singularities, Applications, page 27",
          "text": "A differential operator P#x5C;left(D#x5C;right) is hypoelliptic if for any domain ⊂ #x5C;mathbb#x7B;R#x7D;ⁿ any solution u of the equation P#x5C;left(D#x5C;right)u#x3D;0 from the class #x5C;mathfrak#x7B;D#x7D;'#x5C;left(#x5C;Omega#x5C;right) is a function from C#x5C;infty(ω) for any open set ω ⊂⊂ #x5C;Omega.\nA complete algebraic description of all hypoelliptic differential operators has been obtained by Hörmander in [H1].",
          "type": "quotation"
        },
        {
          "ref": "1998, L. Hörmander, The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis, page 251",
          "text": "Secondly, differential operators and to some extent their fundamental solutions are local even with respect to the wave front set.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "An operator defined as a function of the differentiation operator (the operator which maps functions to their derivatives)."
      ],
      "hyponyms": [
        {
          "word": "Laplace operator"
        },
        {
          "word": "Laplacian"
        },
        {
          "word": "d'Alembert operator"
        },
        {
          "word": "d'Alembertian"
        }
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          "mathematics",
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          "mathematical analysis",
          "mathematical analysis"
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        [
          "operator",
          "operator"
        ],
        [
          "function",
          "function"
        ],
        [
          "differentiation",
          "differentiation"
        ],
        [
          "derivative",
          "derivative#English"
        ]
      ],
      "raw_glosses": [
        "(mathematics, mathematical analysis) An operator defined as a function of the differentiation operator (the operator which maps functions to their derivatives)."
      ],
      "related": [
        {
          "word": "partial differential operator"
        },
        {
          "word": "pseudodifferential operator"
        }
      ],
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        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "differential operator"
      ]
    }
  ],
  "word": "differential operator"
}

{
  "forms": [
    {
      "form": "differential operators",
      "tags": [
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      "expansion": "differential operator (plural differential operators)",
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  "hyponyms": [
    {
      "word": "Laplace operator"
    },
    {
      "word": "Laplacian"
    },
    {
      "word": "d'Alembert operator"
    },
    {
      "word": "d'Alembertian"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "partial differential operator"
    },
    {
      "word": "pseudodifferential operator"
    }
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      "examples": [
        {
          "text": "Define P(D) to be the differential operator given by P(D)#x3D;D²#x2B;5D#x2B;6, where D is the differentiation operator. Then P(D)(#x5C;sin(x))#x3D;-#x5C;sin(x)#x2B;5#x5C;cos(x)#x2B;6.",
          "type": "example"
        },
        {
          "ref": "2000, S. Albeverio, P. Kurasov, Singular Perturbations of Differential Operators, page 328",
          "text": "[…]these conditions appeared in the very first papers on ordinary differential operators.",
          "type": "quotation"
        },
        {
          "ref": "2012, Youri Egorov, Bert-Wolfgang Schulze, Pseudo-Differential Operators, Singularities, Applications, page 27",
          "text": "A differential operator P#x5C;left(D#x5C;right) is hypoelliptic if for any domain ⊂ #x5C;mathbb#x7B;R#x7D;ⁿ any solution u of the equation P#x5C;left(D#x5C;right)u#x3D;0 from the class #x5C;mathfrak#x7B;D#x7D;'#x5C;left(#x5C;Omega#x5C;right) is a function from C#x5C;infty(ω) for any open set ω ⊂⊂ #x5C;Omega.\nA complete algebraic description of all hypoelliptic differential operators has been obtained by Hörmander in [H1].",
          "type": "quotation"
        },
        {
          "ref": "1998, L. Hörmander, The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis, page 251",
          "text": "Secondly, differential operators and to some extent their fundamental solutions are local even with respect to the wave front set.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "An operator defined as a function of the differentiation operator (the operator which maps functions to their derivatives)."
      ],
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          "function",
          "function"
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          "differentiation",
          "differentiation"
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        [
          "derivative",
          "derivative#English"
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        "(mathematics, mathematical analysis) An operator defined as a function of the differentiation operator (the operator which maps functions to their derivatives)."
      ],
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  "word": "differential operator"
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