differential operator
English
Noun
differential operator (plural differential operators)
- (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, page 251:
- Secondly, differential operators and to some extent their fundamental solutions are local even with respect to the wave front set.
Hyponyms
- Laplace operator, Laplacian
- d'Alembert operator, d'Alembertian
Related terms
- partial differential operator
- pseudodifferential operator