# Wiener-Hopf factorization of the characteristic function of a Levy process

Given $X_t$ a Levy process and $\Delta$ an interval of time, I have to compute the Wiener-Hopf factorization $\Phi_+$$\Phi_- of$$\Phi(u,q)=1-q\mathbf{E}[e^{iuX_{\Delta}}]=1-q\varphi(u)=\Phi_+(u,q)\Phi_-(u,q)$$So given$\varphi$the characteristic function of$X_\Delta$, I have to find$\Phi_+$and$\Phi_-\$, not necessarily in an explicit form. Any help is appreciated.