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Is there a term to describe a mapping of a set of functions to another set of functions?

The derivative is an example of what I’m thinking of. Taking the derivative of a function gives a new function based on the old function.

Frasch
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    Not really, as far as I'm aware. The derivative can (and often is) thought of as a function in itself, taking the set of differentiable functions on a set domain, to the set of real functions on that domain. Sometimes it's called an "operator", though this is less to do with a function on a set of functions as it is to do with a function on a vector space (which such sets of functions tend to be). But no, as far as I'm aware, there is no dedicated term for a function between sets of functions. – Theo Bendit Jul 30 '19 at 15:19
  • A mapping is a mapping is a mapping... In some context (computer science) Functional is used. – Mauro ALLEGRANZA Jul 30 '19 at 15:19

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We can consider the vector space of functions between two sets $X, Y$; known as a function space.
Then the mappings between these functions would be linear transformations.

If the domain $X$ is also vector space, the set of linear maps from $X$ to $Y$ form a vector space over the underlying field, denoted $Hom(X,Y)$. One such space is the dual space of $Y$.

Other than that, not really.

Matthew
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There are many words relevant here, Operator and Transform come to mind. For instance, taking a derivative is an example of a differential operator. We can also take the Fourier or Laplace transform of a function.

Brian McDonald
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