The De Rham-Hodge-Skrypnik theory of Delsarte transmutation operators in multidimension and its applications. Part 1
Y.A. Prykarpatsky, A.M. Samoilenko, A. K. Prykarpatsky
TL;DR
This paper explores the spectral properties and geometric structure of Delsarte transmutation operators in multiple dimensions, linking them to De Rham-Hodge-Skrypnik theory of differential complexes.
Contribution
It introduces a novel connection between Delsarte transmutation operators and De Rham-Hodge-Skrypnik theory, expanding understanding of their multidimensional spectral and topological properties.
Findings
Spectral properties of Delsarte transmutation operators are characterized.
Their differential geometric and topological structures are analyzed in multidimension.
Relationships with De Rham-Hodge-Skrypnik theory are established.
Abstract
Spectral properties od Delsarte transmutation operators are studied, their differential geometrical and topological structure in multidimension is analyzed, the relationships with De Rham-Hodge-Skrypnik theory of generalized differential complexes is stated.
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