I'm reading through some material on wavelet and I'm finding it difficult to see why the following is true.
Let $\Psi(\omega)$ is the Fourier transform of the mother wavelet $\psi(t)$
then many paper on wavelet would immediate jump to, is obvious that:
But wouldn't the above yield a 0/0 condition?
I've also tried relaxing the limits and take a derivative on both side, but this would only imply that the mother wavelet is zero at some frequency $\omega$ not $\omega$ = 0. How do you rigorously prove the above relation?