In mathematics, an operator or transform is a function from one space of functions to another. Operators occur commonly in engineering, physics and mathematics. Many are integral operators and differential operators. In the following L is an operator
L : F → G {\displaystyle L:{\mathcal {F}}\to {\mathcal {G}}}
which takes a function y ∈ F {\displaystyle y\in {\mathcal {F}}} to another function L [ y ] ∈ G {\displaystyle L[y]\in {\mathcal {G}}} . Here, F {\displaystyle {\mathcal {F}}} and G {\displaystyle {\mathcal {G}}} are some unspecified function spaces, such as Hardy space, Lp space, Sobolev space, or, more vaguely, the space of holomorphic functions.
See also List of transforms List of Fourier-related transforms Transfer operator Fredholm operator Borel transform Glossary of mathematical symbols