The generalized De Rham-Hodge theory of Delsarte transmutation operators in multidimension case and its applications

Abstract

A study of spectral and differential-geometric properties of Delsarte transmutation operators 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.