The study of Delsarte-Lions type binary transformations, their differential-geometric and operator structure with applications. Part 2

Abstract

The Gelfand-Levitan integral equations for Delsarte-Lions type transformations in multidimension are studied. The corresponding spectral and analytical properties of Delsarte-Lions transformed operators are analyzed by means of the differential-geometric and topological tools. An approach for constructing Delsarte-Lions type transmutation operators for multidimensional differential expressions is devised.

Keywords

• Delsarte transmutation operators
• generalized de Rham-Hodge differential complex
• Delsarte-Lions type transformations
• Gelfand-Levitan-Marchenko type integral equations
• multidimensional differential operator pencils