differential operator
noun1
Mathematical analysis, Mathematics, Sciences An 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.
- […]these conditions appeared in the very first papers on ordinary differential operators.2000, S. Albeverio, P. Kurasov, Singular Perturbations of Differential Operators, page 328:
2 more examples
- 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:
- Related terms
- partial differential operator, pseudodifferential operator