Opuscula Math. 27, no. 1 (2007), 113-130
The study of Delsarte-Lions type binary transformations, their differential-geometric and operator structure with applications. Part 2
Yarema A. Prykarpatsky
Anatoliy M. Samoilenko
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.
Mathematics Subject Classification: 34A30, 34B05, 34B15.