Theory of Multidimensional Delsarte–Lions Transmutation Operators. II

A. M. Samoilenko , Yarema A. Prykarpatskyy , D. Blackmore , Anatolij K. Prykarpatsky


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 suitable 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. The soliton solutions are discussed for a certain class of dynamical systems.
Author A. M. Samoilenko
A. M. Samoilenko,,
, Yarema A. Prykarpatskyy (FoEEaLS / DoAM)
Yarema A. Prykarpatskyy,,
- Department of Applied Mathematics
, D. Blackmore
D. Blackmore,,
, Anatolij K. Prykarpatsky
Anatolij K. Prykarpatsky,,
Journal seriesUkrainian Mathematical Journal, ISSN 0041-5995, e-ISSN 1573-9376, (N/A 40 pkt)
Issue year2019
Publication size in sheets1.7
ASJC Classification2600 General Mathematics
Languageen angielski
Score (nominal)40
Score sourcejournalList
Publication indicators WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 0.554; WoS Impact Factor: 2018 = 0.345 (2) - 2018=0.37 (5)
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Oświadczenie o afiliacjiYa. A. Prykarpatsky
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