# Wavelets frame for $L^2[0,\infty)$

I need a wavelet frame for $L^2[0,\infty)$. Moreover, the wavelet should be twice differentiable and with continuous second order derivatives. Hopefully, the wavelet should have compact support (either in the time-domain or in the frequency-domain). Is there such a wavelet?

Previously I had asked similar questions here and here. However I think this question fits well here.

Thanks.

• In Daubechies' "Ten lectures on wavelets", section 10.7, an orthonormal wavelet basis for $L_2[0,\infty]$ is constructed, some references are given. Have you seen this? – faleichik Feb 16 '12 at 12:29
• sorry for wrong ] bracket :-) – faleichik Feb 16 '12 at 17:29