Integral transform

There are many classes of problems that are difficult to solve—or at least quite unwieldy algebraically—in their original representations. An integral transform "maps" an equation from its original "domain" into another domain, in which manipulating and solving the equation may be much easier than in the original domain. The solution can then be mapped back to the original domain with the inverse of the integral transform.

Note that there are alternative notations and conventions for the Fourier transform.

Here integral transforms are defined for functions on the real numbers, but they can be defined more generally for functions on a group.