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\end{eqnarray}  In the frequency domain the product of these two functions read:  \begin{eqnarray}  N(\omega)=(e^2/h)\sum_{k\beta,q\gamma} \int \frac{d\epsilon}{2\pi} V_{\beta k} V^*_{\gamma q}G_{\beta q}>(\omega+\epsilob) q}>(\omega+\epsilon)  G^{h,<}_{\gamma k}(\epsilon) \end{eqnarray}  where  \begin{eqnarray} 
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\begin{eqnarray}  G^{<,h}_{\gamma k}(\omega) = \sum_\beta [G_{\gamma\beta}^r(\omega) V_{\beta k} g^{<,h}_{k}(\omega)+ G_{\gamma\beta}^<(\omega) V_{\beta k} g^{a,h}_{k}(\omega)]  \end{eqnarray}  Then, we have  \begin{eqnarray}  &&N(\omega)=(e^2/h)\sum_{k\beta,q\gamma, \nu\mu} \int \frac{d\epsilon}{2\pi} V_{\beta k} V^*_{\gamma q}   \\ \nonumber  &&[G_{\beta\nu}^r(\omega+\epsilon) V_{\nu q} g^{>}_{q}(\omega+\epsilon)+ G_{\beta\nu}^>(\omega+\epsilon) V_{\nu q} g^{a}_{q}(\omega+\epsilon)]   \\ \nonumber  &&[G_{\gamma\mu}^r(\omega) V_{\mu k} g^{<,h}_{k}(\omega)+ G_{\gamma\mu}^<(\omega) V_{\mu k} g^{a,h}_{k}(\omega)]