# Definition:Integral Transform/Operator

Jump to navigation
Jump to search

## Definition

Let $F \left({p}\right)$ be an integral transform:

- $F \left({p}\right) = \displaystyle \int_a^b f \left({x}\right) K \left({p, x}\right) \, \mathrm d x$

This can be written in the form:

- $F = T \left({f}\right)$

where $T$ is interpreted as the (unitary) operator meaning:

*Multiply this by $K \left({p, x}\right)$ and integrate {with respect to $x$ between the limits $a$ and $b$.*

Thus $T$ transforms the function $f \left({x}\right)$ into its image $F \left({p}\right)$, which is itself another real function.

## Also denoted as

$F = T \left({f}\right)$ can be seen presented as $F = T f$ by some sources.

## Sources

- 1968: Peter D. Robinson:
*Fourier and Laplace Transforms*... (previous) ... (next): $\S 1.1$. The Idea of an Integral Transform