Inverse transform

Summary

The inverse transform of an integral transform $T$ recovers a function $f$ from its image $Tf$. It exists when $T$ is one-to-one on the class of functions in use. Often the inverse is itself an integral transform with its own kernel. Examples are the Fourier inversion formula and the Bromwich integral for the inverse Laplace transform. A typical use of a transform is: transform the problem, solve it on the transform side, then apply the inverse transform.