  We present a theoretical approach to determine the electronic properties of
nanoscale systems exhibiting strong electron-electron and electron-phonon
interactions and coupled to metallic electrodes. This approach is based on an
interpolative ansatz for the electronic self-energy which becomes exact both in
the limit of weak and strong coupling to the electrodes. The method provides a
generalization of previous interpolative schemes which have been applied to the
purely electronic case extensively. As a test case we consider the single level
Anderson-Holstein model. The results obtained with the interpolative ansatz are
in good agreement with existing data from Numerical Renormalization Group
calculations. We also check our results by considering the case of the
electrodes represented by a few discrete levels which can be diagonalized
exactly. The approximation describes properly the transition from the Kondo
regime where electron-electron interactions dominate to the polaronic case
characterized by a strong electron-phonon interaction.
