I was just thinking back to my advanced linear algebra class and I remember the prof mumbling something about the fourier series being an orthonormal basis for the hilbert space of square-integrable real-valued functions, lebesgue something, etc., and demonstrating the properties of the integral inner product and projections into that space. It all made sense at the time, I think. :) Sorry if I'm kinda vague, I can provide more info if needed. I am curious, though, if something similar exists for laplace transform. It certainly looks like it fits the form, but I have been unable to find any detailed analysis of such. Anyone have insight?