This tag is for questions relating to integral operators, which are an important special class of linear operators that act on function spaces.
Integral operators are particular types of operators on $~L^p(E)~$.
Let $~k~$ be a fixed measurable function on $~\mathbb R^2~$. The integral operator $~L_k~$ with kernel $~k~$ is formally defined by$$L_kf(x)=\int_{-\infty}^{+\infty}k(x,y)~f(y)~dy\tag1$$
i.e., if $~f~$ is a measurable function on $~\mathbb R~$, then $~L_kf~$ is the function defined by equation $(1)$, as long as this integral is well-defined for a.e. $~x ∈ \mathbb R~$ .
Otherwise $~L_kf~$ is not defined.
Note: An integral operator is a natural generalization of the ordinary matrix-vector product.
References:
https://www.encyclopediaofmath.org/index.php/Integral_operator
