\langle \tilde{g}(\omega_1)...\tilde{g}(\omega_k)\rangle = \langle H(\omega_1) \tilde{f}(\omega_1)... H(\omega_k) \tilde{f}(\omega_k)\rangle = H(\omega_1)...H(\omega_k) \langle\tilde{f}(\omega_1)...\tilde{f}(\omega_k)\rangle