'Any periodic function which follows Dirichlet's conditions can be expressed as a Fourier series.'
Is there any mathematical proof to validate this? Even if not a proof per se, how to convince oneself intuitively of this statement? I did read about Fourier experimentally arriving at the series from the heat equation, but how did he ascertain that any periodic function which follows certain criteria (Dirichlet's conditions) can be expressed as one such series.
I understand it is true, but is there any way to actually believe this intuitively?
As in, just looking at a square wave which is periodic, how do I ascertain that it is made up of innumerable sine and cosine waves?
Am quite interested to know about this.