[en] A dynamical scheme based on the equation for the T-matrix momentum-transfer spectral density and a new class of integral representations for the Jost function (matrix) is proposed for the Schroedinger and Dirac Hamiltonians in spaces of arbitrary dimension N with a local and nonlocal generalized Yukawa potential and in the model with N coupled channels. The off-shell Jost-function method is generalized for these Hamiltonians, and a universal renormalization procedure is presented to define them for singular and nonlocal potentials. 52 refs