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 | |||
| Geometric integral | |||
| Bigeometric integral | |||
| Logarithmic derivative | |||
| Elasticity | |||
| Schwarzian derivative | |||
| Geometric derivative | |||
| Bigeometric derivative | |||
| Total variation | |||
| Arithmetic mean | |||
| Geometric mean | |||
| Cartesian | Subtangent | ||
| Parametric Cartesian |
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| Polar | |||
| Polar | Sector area | ||
| Cartesian | Arc length | ||
| Parametric Cartesian |
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| Polar | |||
| Cartesian | Affine arc length | ||
| Parametric Cartesian |
|||
| Parametric Cartesian |
|||
| Cartesian | Curvature | ||
| Parametric Cartesian |
|||
| Polar | |||
| Parametric Cartesian |
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| Cartesian | Affine curvature | ||
| Parametric Cartesian |
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| 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) |
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| Distribution functionals | |||
| Convolution | |||
| Differential entropy | |||
| Expected value | |||
| Variance | |||
Famous quotes containing the words list of and/or list:
“Shea—they call him Scholar Jack—
Went down the list of the dead.
Officers, seamen, gunners, marines,
The crews of the gig and yawl,
The bearded man and the lad in his teens,
Carpenters, coal-passers—all.”
—Joseph I. C. Clarke (1846–1925)
“Shea—they call him Scholar Jack—
Went down the list of the dead.
Officers, seamen, gunners, marines,
The crews of the gig and yawl,
The bearded man and the lad in his teens,
Carpenters, coal-passers—all.”
—Joseph I. C. Clarke (1846–1925)