[tzahola]

Hmmm. I think it’s easy to fix that:

Suppose that there’s a function f, that can be written as an infinite sum (integral) of shifted Dirac impulses, but cannot be written in your representation as a sum of those “base functions”. Then simply add a new dimension to your representation that will correspond to f, so that f will be represented as 1 at this new dimension, and zero everywhere else. (In other words: add f to the base functions)

Repeat until you have covered every function.