List of operators
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
- List of transforms
- List of Fourier-related transforms
- Transfer operator
- Fredholm operator
- Borel transform
- Table of mathematical symbols
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