  The structure properties of multidimensional Delsarte transmutation operators
in parametirc functional spaces are studied by means of differential-geometric
tools. It is shown that kernels of the corresponding integral operator
expressions depend on the topological structure of related homological cycles
in the coordinate space. As a natural realization of the construction presented
we build pairs of Lax type commutive differential operator expressions related
via a Darboux-Backlund transformation having a lot of applications in solition
theory. Some results are also sketched concerning theory of Delsarte
transmutation operators for affine polynomial pencils of multidimensional
differential operators.
