differential operator

plural differential operators

1. mathematical analysisAn operator defined as a function of the differentiation operator (the operator which maps functions to their derivatives).

   Define P(D) to be the differential operator given by P(D)#61;D²#43;5D#43;6, where D is the differentiation operator. Then P(D)(#92;sin(x))#61;-#92;sin(x)#43;5#92;cos(x)#43;6.

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   […]these conditions appeared in the very first papers on ordinary differential operators.

   2000, S. Albeverio, P. Kurasov, Singular Perturbations of Differential Operators, page 328

   A differential operator P#92;left(D#92;right) is hypoelliptic if for any domain ⊂ #92;mathbb#123;R#125;ⁿ any solution u of the equation P#92;left(D#92;right)u#61;0 from the class #92;mathfrak#123;D#125;'#92;left(#92;Omega#92;right) is a function from C#92;infty(ω) for any open set ω ⊂⊂ #92;Omega. A complete algebraic description of all hypoelliptic differential operators has been obtained by Hörmander in [H1].

   2012, Youri Egorov, Bert-Wolfgang Schulze, Pseudo-Differential Operators, Singularities, Applications, page 27

   Secondly, differential operators and to some extent their fundamental solutions are local even with respect to the wave front set.

   1998, L. Hörmander, The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis, page 251