An integral operator is an
operator that involves
integration
Integration may refer to:
Biology
*Multisensory integration
*Path integration
* Pre-integration complex, viral genetic material used to insert a viral genome into a host genome
*DNA integration, by means of site-specific recombinase technology, ...
. Special instances are:
* The operator of integration itself, denoted by the
integral symbol
The integral symbol:
: (Unicode), \displaystyle \int (LaTeX)
is used to denote integrals and antiderivatives in mathematics, especially in calculus.
History
The notation was introduced by the German mathematician Gottfried Wilhelm Leibniz in 1 ...
*
Integral linear operator
An integral bilinear form is a bilinear functional that belongs to the continuous dual space of X \widehat_ Y, the injective tensor product of the locally convex topological vector spaces (TVSs) ''X'' and ''Y''. An integral linear operator is a co ...
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 pre ...
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 linear i ...
s involving integrals
*
Integral transform
In mathematics, an integral transform 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 characterized and manipulated than in ...
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 vect ...
s, which involve integrals
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Integral calculus