In my book the dirac delta is described by the equation on the attached picture. This realtion is derived from the fourier transform, but I'm not sure that I understand what it says. If u=t it is clear that one gets f(u) in the fourier inversion theorem. But why wouldn't u=t? In the derivation of the fourier transform from the discrete fourier series t was just changed to u in the expression of the coefficients to avoid confusion. Can anyone try to picture what this expression fundamentally says? I should suspect that it is like the analogue of the ortogonality relation of the discrete fourier series, but I can't quite understand it. And what would the situation u≠t represent?