Comparison of different types of Fourier transforms theory.

One of the contributions of postwar pure mathematics to applied sciences is connected with the theory of generalised functions (distribution theory). In fact, applications of this theory are numerous in physics, in nonlinear mechanics, in fluid dynamics, and in field theory. Furthermore, dubious tricks (more than 50 years ago, Heaviside introduced his rules on symbolic calculus in a daring report, where mathematical operations that are hardly justified are performed in the solving of problems of physics; Dirac delta function; differentiation of non-differentiable functions; the free use of diverging Fourier series and integrals;) physicists have resorted to up to now are simply and rigorously justified