Theory of multidimensional Delsarte – Lions transmutation operators. II
The differential-geometric and topological structures related to the Delsarte transmutation operators and the Gelfand – Levitan – Marchenko equations that describe these operators are studied by using sutable differential de Rham – Hodge – Skrypnik complexes. The correspondence between the spectral theory and special Berezansky-type congruence properties of the Delsarte transmutation operators is established. Some applications to multidimensional differential operators are presented, including the three-dimensional Laplace operator, the two-dimensional classical Dirac operator, and its multidimensional affine extension associated with self-dual Yang – Mills equations. Soliton solutions of a certain class of dynamical systems are discussed.
How to Cite
Blackmore, D., A. K. Prykarpatsky, Y. A. Prykarpatsky, and A. M. Samoilenko. “Theory of Multidimensional Delsarte – Lions Transmutation Operators. II”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 6, June 2019, pp. 808-39, https://umj.imath.kiev.ua/index.php/umj/article/view/1478.