Recent experimental data on electron transport through molecules and quantum dots have allowed to observe phonon satellites in the Kondo regime. Transport through a quantum dot attached to non-magnetic or ferromagnetic electrodes is studied theoretically within the non-equilibrium Green function formalism and effects of local vibrational modes are analyzed for different values of parameter g describing the coupling strength of electron-phonon systems. A presence of phonons strongly influences the spectral function and the differential conductance leading to an appearance of phonon satellites on both sides of the main Kondo anomaly. When the dot is attached to ferromagnetic electrodes with parallel magnetic moments the Kondo resonance is split due to the effective field generated by electrodes. The main components move away from the zero bias limit as polarization of electrodes increases. The Kondo satellites move accordingly and develop in a distance equal to the phonon energy from each Kondo component. The Kondo effect is strongly reduced due to polarization of electrodes and due to coupling to phonon bath. In systems in which spin voltage V_s  is applied together with transport voltage V_e spin current I_s and charge current I_e can be carried out. The influence of electron-phonon coupling on the spin conductance G_s=dI_s/dV_s and the charge conductance G_e=dI_e/dV_s is discussed in detail. G_s reveals the dependence similar to that found for junction with ferromagnetic electrodes with two Kondo resonances accompanied by phonon satellites, but quite different behaviour is obtained for the charge conductance.

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1. Electron Transport Through Nanoscopic Spin Valves