An integral operator is an
operator that involves
integration. Special instances are:
* The operator of integration itself, denoted by the
integral symbol
The integral symbol (''see below'') is used to denote integrals and Antiderivative, antiderivatives in mathematics, especially in calculus.
History
The notation was introduced by the Germany, German mathematician Gottfried Wilhelm Leibniz i ...
*
Integral linear operator
In mathematical analysis, an integral linear operator is a linear operator ''T'' given by integration; i.e.,
:(Tf)(x) = \int f(y) K(x, y) \, dy
where K(x, y) is called an integration kernel.
More generally, an integral bilinear form is a bilinea ...
s, which are
linear operator
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that pr ...
s induced by
bilinear form
In mathematics, a bilinear form is a bilinear map on a vector space (the elements of which are called '' vectors'') over a field ''K'' (the elements of which are called '' scalars''). In other words, a bilinear form is a function that is linea ...
s involving integrals
*
Integral transform
In mathematics, an integral transform is a type of transform that maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily charac ...
s, which are maps between two
function space
In mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is inherited by the function space. For example, the set of functions from any set into a ve ...
s, which involve integrals
{{Authority control
Integral calculus