Differential operator

A harmonic function defined on an annulus. Harmonic functions are exactly those functions which lie in the kernel of the Laplace operator, an important differential operator.

In mathematics, a differential operator is an operator defined as a function of the differentiation operator (which is an operation that accepts a function and returns another function, i.e. a higher-order function).

This article considers mainly linear differential operators, which are the most common type. However, non-linear differential operators also exist, such as the Schwarzian derivative.