Definition:Inversion Theorem

Definition
Let $\map F p$ be an integral transform:


 * $\map F p = \displaystyle \int_a^b \map f x \map K {p, x} \, \mathrm d x$

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:
 * $\map f x = \displaystyle \int_\alpha^\beta \map F p \map H {x, p} \, \mathrm d p$

should such an $\map H {x, p}$ exist.

It is not necessarily the case that it does exist..