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.
About the authors ▼
Yarema A. Prykarpatsky
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland; The Institute of Mathematics at the NAS, Kiev 01601, Ukraine
Anatoliy M. Samoilenko
The Institute of Mathematics at the NAS, Kiev 01601, Ukraine
About the article ▼
Received: 2006-04-26.
Cite this article as ▼
Yarema A. Prykarpatsky, Anatoliy M. Samoilenko, The study of Delsarte-Lions type binary transformations, their differential-geometric and operator structure with applications. Part 2, Opuscula Math. 27, no. 1 (2007), 113-130,
http://dx.doi.org/10.7494/OpMath.2007.27.1.113.
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