High-order non symmetric difference operators with complex coefficients
are considered. The correspondence between dynamics of the coefficients of
the operator defined by a Lax pair and its resolvent function is established. The
method of investigation is based on the analysis of the moments for the operator.
The solution of a discrete dynamical system is studied. We give explicit expressions
for the resolvent function and, under some conditions, the representation of the
vector of functionals, associated with the solution for the integrable systems
