List of mathematic 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 Curvedefinition Variables DescriptionLinear 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 operatorNon-linear transformations Inverse function Legendre transformation Left composition Indefinite product Logarithmic derivative Elasticity Schwarzian derivative Total variation Arithmetic mean Geometric mean CartesianSubtangent ParametricCartesian Polar Polar Sector area CartesianArc length ParametricCartesian Polar CartesianAffine arc length ParametricCartesian ParametricCartesian CartesianCurvature ParametricCartesian Polar ParametricCartesian CartesianAffine curvature ParametricCartesian ParametricCartesianTorsion of curves ParametricCartesianDual curve(tangent coordinates) ParametricCartesianParallel curve ParametricCartesianEvolute Intrinsic ParametricCartesianInvolute ParametricCartesianPedal curve with pedal point (0;0) ParametricCartesianNegative pedal curve with pedal point (0;0) IntrinsicIntrinsic toCartesiantransformationMetric 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 Glossary of mathematical symbols