Admissibility condition for wavelets

Summary

The admissibility condition asks that a function $\psi$ in $L^2(\R)$ have finite constant $C_\psi = \int \abs{\hat\psi(\xi)}^2 / \abs{\xi} \, d\xi$. It makes the continuous wavelet transform with respect to $\psi$ preserve energy up to the factor $C_\psi$. So the transform can be inverted. For integrable $\psi$ it forces $\int \psi = 0$: an admissible function must oscillate.