An operator 
assigns to every function 
a function 
.
It is therefore a mapping between two function spaces.
If the range is on the real line or in the complex
plane, the mapping is usually called a functional
instead.
Operator
See also
Biharmonic Operator, Binary Operator, Casimir Operator, Convective Operator, d'Alembertian, Delta Operator, Functional Analysis, Hecke Operator, Hermitian Operator, Identity Operator, Lambda Calculus, Laplacian, Laplace-Beltrami Operator, Linear Operator, Operand, Operator Spectrum, Operator Theory, Perron-Frobenius Operator, Projection Operator, Rotation Operator, Scattering Operator, Shift-Invariant Operator, Shift Operator, Theta Operator, Umbral Operator, Vector Laplacian, Wave Operator, Weierstrass OperatorExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Operator." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Operator.html