The article is some summary of a book with chapters. At some point they limit the space to the subspace of functions periodic over (b-a) and change the basis (w

The article is some summary of a book with chapters. At some point they limit the space to the subspace of functions periodic over (b-a) and change the basis (with proof) from dirac delta to sines of frequency 2pi*k/(b-a) [with k in N]. In this subspace all functions have Fourier transformations.