  We review how some multianalytic inner functions of the Beurling type theorem
are associated to row contractions following works of G.Popescu. Motivated by a
result on weak Markov dilations, we define a notion of characteristic function
for ergodic and coisometric row contractions with a one-dimensional invariant
subspace for the adjoints. Our characteristic function is a complete unitary
invariant for such tuples. Thereafter we extend the analysis of characteristic
functions to contractive liftings of row contractions. We apply our theory to
completely positive maps and explore applications to fixed point sets of
completely positive maps related to each other by a subisometric lifting. In
the last two chapter we consider constrained row contractions and some module
structures in this context.
