\begin{definition}[Definition:Integral Transform/Operator]
Let $\map F p$ be an integral transform:
:$\map F p = \ds \int_a^b \map f x \map K {p, x} \rd x$
This can be written in the form:
:$F = \map T f$
where $T$ is interpreted as the (unitary) operator meaning:
:''Multiply this by $\map K {p, x}$ and integrate {{WRT|Integration}} $x$ between the limits $a$ and $b$.''
Thus $T$ transforms the function $\map f x$ into its image $\map F p$, which is itself another real function.
{{expand|The specific domain and codomain of $T$ need to be defined in order to make this rigorous.}}
\end{definition}