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Differential operators


In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and returns another function (in the style of a higher-order function in computer science).

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

Assume that there is a map from a function space to another function space and a function so that is the image of i.e.,  A differential operator is represented as a linear combination, finitely generated by and its derivatives containing higher degree such as


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