List of operators
From Infogalactic: the planetary knowledge core
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 | |||
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Derivative of nth order | ||
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Cartesian | ![]() ![]() |
Integral, area |
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Composition operator | ||
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Even component | ||
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Odd component | ||
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Difference operator | ||
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Backward difference (Nabla operator) | ||
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Indefinite sum operator (inverse operator of difference) | ||
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Sturm–Liouville operator | ||
Non-linear transformations | |||
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Inverse function | ||
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Legendre transformation | ||
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Left composition | ||
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Indefinite product | ||
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Logarithmic derivative | ||
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Elasticity | ||
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Schwarzian derivative | ||
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Total variation | ||
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Arithmetic mean | ||
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Geometric mean | ||
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Cartesian | ![]() ![]() |
Subtangent |
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Parametric Cartesian |
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|
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Polar | ![]() ![]() |
|
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Polar | ![]() ![]() |
Sector area |
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Cartesian | ![]() ![]() |
Arc length |
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Parametric Cartesian |
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|
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Polar | ![]() ![]() |
|
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Cartesian | ![]() ![]() |
Affine arc length |
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Parametric Cartesian |
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Parametric Cartesian |
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|
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Cartesian | ![]() ![]() |
Curvature |
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Parametric Cartesian |
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|
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Polar | ![]() ![]() |
|
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Parametric Cartesian |
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|
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Cartesian | ![]() ![]() |
Affine curvature |
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Parametric Cartesian |
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Parametric Cartesian |
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Torsion of curves |
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Parametric Cartesian |
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Dual curve (tangent coordinates) |
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Parametric Cartesian |
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Parallel curve |
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Parametric Cartesian |
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Evolute |
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Intrinsic | ![]() ![]() |
|
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Parametric Cartesian |
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Involute |
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Parametric Cartesian |
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Pedal curve with pedal point (0;0) |
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Parametric Cartesian |
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Negative pedal curve with pedal point (0;0) |
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Intrinsic | ![]() ![]() |
Intrinsic to Cartesian transformation |
Metric functionals | |||
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Norm | ||
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Inner product | ||
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Fubini–Study metric (inner angle) |
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Distribution functionals | |||
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Convolution | ||
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Differential entropy | ||
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Expected value | ||
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Variance |