  We consider simultaneously two different reductions of a Zakharov-Shabat's
spectral problem in pole gauge. Using the concept of gauge equivalence, we
construct expansions over the eigenfunctions of the recursion operators related
to the afore-mentioned spectral problem with arbitrary constant asymptotic
values of the potential functions. In doing this, we take into account the
discrete spectrum of the scattering operator. Having in mind the applications
to the theory of the soliton equations associated to the GMV systems, we show
how these expansions modify depending on the symmetries of the functions we
expand.
