De Rham-Hodge-Skrypnik theory. A survey of the spectral and differential   geometric aspects of the De Rham-Hodge-Skrypnik theory related with Delsarte   transmutation operators in multidimension and its applications to spectral   and soliton problems. Part 1
  A review on spectral and differential-geometric properties of Delsarte transmutation operators in multidimension is given. Their differential geometrical and topological structure in multidimension is analyzed, the relationships with De Rham-Hodge-Skrypnik theory of generalized differential complexes are stated. Some applications to integrable dynamical systems theory in multidimension are presented. 
Y.A. Prykarpatsky, A.M. Samoilenko, A. K. Prykarpatsky