List of operators

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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

which takes a function to another function . Here, and are some unspecified function spaces, such as Hardy space, Lp space, Sobolev space, or, more vaguely, the space of holomorphic functions.

Expression Curve
definition
Variables Description
Linear transformations
Derivative of nth order
Cartesian
Integral, area
Composition operator
Even component
Odd component
Difference operator
Backward difference (Nabla operator)
Indefinite sum operator (inverse operator of difference)
Sturm–Liouville operator
Non-linear transformations
Inverse function
Legendre transformation
Left composition
Indefinite product
Logarithmic derivative
Elasticity
Schwarzian derivative
Total variation
Arithmetic mean
Geometric mean
Cartesian
Subtangent
Parametric
Cartesian

Polar
Polar
Sector area
Cartesian
Arc length
Parametric
Cartesian

Polar
Cartesian
Affine arc length
Parametric
Cartesian

Parametric
Cartesian


Cartesian
Curvature
Parametric
Cartesian

Polar
Parametric
Cartesian


Cartesian
Affine curvature
Parametric
Cartesian

Parametric
Cartesian


Torsion of curves


Parametric
Cartesian

Dual curve
(tangent coordinates)


Parametric
Cartesian

Parallel curve


Parametric
Cartesian

Evolute
Intrinsic


Parametric
Cartesian

Involute


Parametric
Cartesian

Pedal curve with pedal point (0;0)


Parametric
Cartesian

Negative pedal curve with pedal point (0;0)


Intrinsic
Intrinsic to
Cartesian
transformation
Metric functionals
Norm
Inner product
Fubini–Study metric
(inner angle)
Distribution functionals
Convolution
Differential entropy
Expected value
Variance

See also[edit]