Definition:Integral Transform/Operator

Definition
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 $x$ 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.

Also denoted as
$F = \map T f$ can be seen presented as $F = T f$ by some sources.