BIBO stability

There are cases in which the Fourier transform doesn't converge uniformly, but it does converge in some other sense if it is square-summable (i.e. it has finite energy). In these cases, the transform converges to a discontinuous function. If the Fourier transform is not continuous, then you know that its inverse is not in the sequence space. So one can judge the stability of a system by looking at the continuity of its transfer function. (Main reason is that the

Delta function has internal paradox as a function with integral)