\begin{definition}[Definition:Inversion Theorem]
Let $\map F p$ be an integral transform:
:$\map F p = \ds \int_a^b \map f x \map K {p, x} \rd x$
Let $T$ be the integral operator associated with $\map F p$:
:$F = \map t F$
An '''inversion theorem''' is a specification for an inverse integral operator $T^{-1}$ of the form $f = \map {T^{-1} } F$ such that:
:$\map f x = \ds \int_\alpha^\beta \map F p \map H {x, p} \rd p$
should such an $\map H {x, p}$ exist.
It is not necessarily the case that it does exist..
\end{definition}