Density of states for energy-dependent effective Hamiltonians

We provide two analytic expressions particularly useful for the evaluation of the density of stares of multichannel interacting structures described b y effective energy-dependent Hamiltonians. We show that the knowledge of th e off-diagonal matrix elements of a properly defined Green's function, betw een the terminal sites of the system, is the main ingredient to obtain the total density of states. We have used our expressions to calculate the dens ities of states of ladder chains where each site of the chains may be conne cted to an external system. A couple of significant examples clarify the fe asibility of these expressions.