>>11688164Well, first off, you should understand that fourier transforms and laplace transforms arise as continuous generalizations of fourier expansions and laplace expansions. The reason people used those expansions was because the functions were solutions to a specific differential equation.
Now, in other differential equations, you have other solutions, and hence other expansions. For example, in the case of a quantum mechanic harmonic oscillator, the solutions are gaussians multiplied by hermite polynomials. Similarly there is a corresponding hermite transform. Just like the fourier transform, your hermite conjugate is no longer a function of x, but rather a parameter of the kernal (n the hermite polynomial index, or in the case of fourier typically k).
So the, if you say that fourier and laplace transforms won't work for you, the first thing to do is look at the specifics of the problem your working on, and figure out what the eigen functions for your problem are. Then generalize to a transform.
