I've been searching all over the Internet for this but without finding a satisfying answer. This might be a dumb question, but I would like to know the answer anyway.
Is there a set of continuous functions which when combined linearly (or not maybe) span all the functions space ? Could we decompose a log, a sine or an exponent to simpler components ? And if not why ?
I know that Fourier analysis is a powerful tool for functions decomposition, but I wanted to know If we could go further and decompose even trigonometric functions. I wondered if there was is theory about this ?
Thanks for any answer.