Definition:Inverse Integral Operator

Definition
Let $T: f \to F$ be an integral operator on a function $f$.

Let there be a (unitary) operator $T^{-1}: F \to f$ such that for a given $F \left({p}\right)$ there exists a unique $f \left({x}\right)$ such that $f = T \left({f}\right)$.

Then $T^{-1}$ is the inverse integral operator of $T$.