Consider the equation
F is a function of a real variable omega ,the function value is a complex number.
is called amplitude specturm of f
F=f(T) means F is the Fourier transform of f as for Laplace transform Laplace transform of f
F is a function of real variable t the function value F(t) is a complex number, F=f(t) means F is the Fourier transform of f as for Laplace transform