I am a mathematician (not that it is relevant) but honestly, "demystifying" seems a bit exaggerated for a piece of commentary which simply makes it all more complicated than it is.
If the aim is to 'abstract' it, then call it 'abstraction' but demystifying is rather far-fetched.
Yes, the Fourier transform is no more than the expression of the elements of a Hilbert space in a complete basis: get over it and move on? Is it clear? You can generalize it even more.
But honestly, as Abhyankar has been quoted saying, the real question is... "What is a polynomial?" That is the really difficult question to answer.
Sorry for the rant but titles should really be at least honest (I agree they have to be attractive but...).
If the aim is to 'abstract' it, then call it 'abstraction' but demystifying is rather far-fetched.
Yes, the Fourier transform is no more than the expression of the elements of a Hilbert space in a complete basis: get over it and move on? Is it clear? You can generalize it even more.
But honestly, as Abhyankar has been quoted saying, the real question is... "What is a polynomial?" That is the really difficult question to answer.
Sorry for the rant but titles should really be at least honest (I agree they have to be attractive but...).