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

Abstract

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.

References in corpus (2)

• The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Part 2
• Differential-geometric and topological structure of multidimensional Delsarte transmutation operators