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An operator $A: f^{(n)}(I) \mapsto f(I)$ assigns to every function $f \in f^{(n)}(I)$ a function $A(f) \in f(I)$. 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.

See also Abstraction Operator, Adjoint Operator, Antilinear Operator, Biharmonic Operator, Binary Operator, Casimir Operator, Convective Operator, d'Alembertian Operator, Difference Operator, Functional Analysis, Hecke Operator, Hermitian Operator, Identity Operator, Laplace-Beltrami Operator, Linear Operator, Operand, Perron-Frobenius Operator, Projection Operator, Rotation Operator, Scattering Operator, Self-Adjoint Operator, Spectrum (Operator), Theta Operator, Wave Operator


Gohberg, I.; Lancaster, P.; and Shivakuar, P. N. (Eds.). Recent Developments in Operator Theory and Its Applications. Boston, MA: Birkhäuser, 1996.

Hutson, V. and Pym, J. S. Applications of Functional Analysis and Operator Theory. New York: Academic Press, 1980.

© 1996-9 Eric W. Weisstein