Differential-geometric and topological structure of multidimensional Delsarte transmutation operators
Yarema Prykarpatsky, Anatoliy Samoilenko, Anatoliy K. Prykarpatsky
TL;DR
This paper explores the differential geometric and topological structures of multidimensional Delsarte transmutation operators and their connections with De Rham-Hodge-Skrypnik theory of differential complexes.
Contribution
It introduces a new framework linking Delsarte transmutation operators with advanced differential complex theories in multiple dimensions.
Findings
Established relationships with De Rham-Hodge-Skrypnik theory
Provided a geometric and topological characterization of the operators
Enhanced understanding of multidimensional transmutation operators
Abstract
A differential geometrical and topological structure of Delsarte transmutation operators in multidimension is studied, the relationships with De Rham-Hodge-Skrypnik theory of generalized differential complexes is stated.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons