differential operator

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English

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Noun

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differential operator (plural differential operators)

  1. (mathematics, mathematical analysis) An operator defined as a function of the differentiation operator (the operator which maps functions to their derivatives).
    Define to be the differential operator given by , where is the differentiation operator. Then .
    • 2000, S. Albeverio, P. Kurasov, Singular Perturbations of Differential Operators, page 328:
      [] these conditions appeared in the very first papers on ordinary differential operators.
    • 2012, Youri Egorov, Bert-Wolfgang Schulze, Pseudo-Differential Operators, Singularities, Applications, page 27:
      A differential operator is hypoelliptic if for any domain ⊂ any solution of the equation from the class is a function from (ω) for any open set ω ⊂⊂ .
      A complete algebraic description of all hypoelliptic differential operators has been obtained by Hörmander in [H1].
    • 1998, L. Hörmander, The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis[1], page 251:
      Secondly, differential operators and to some extent their fundamental solutions are local even with respect to the wave front set.

Hyponyms

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