TY - JOUR
AU - D. Blackmore
AU - A. K. Prykarpatsky
AU - Ya. A. Prykarpatsky
AU - A. M. Samoilenko
PY - 2018/12/25
Y2 - 2020/11/29
TI - Theory
of multidimensional Delsarte – Lions transmutation operators. I
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 70
IS - 12
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1667
AB - We present a brief review of the original results obtained by the authors in the theory of Delsarte –Lions transmutations of multidimensional spectral differential ope rators based on the classical works by Yu. M. Berezansky, V. A. Marchenko, B. M. Levitan, and R. G. Newton, on the well-known L. D. Faddeev’s survey, the book by L. P. Nyzhnyk, and the generalized De-Rham – Hodge theory suggested by I. V. Skrypnik and developed by the authors for the differential-operatorcomplexes. The operator structure of Delsarte – Lions transformations and the properties of their Volterra factorizations are analyzed in detail. In particular, we study the differential-geometric and topological structures of the spectral properties of the Delsarte – Lions transmutations within the framework of the generalized De-Rham – Hodge theory.
ER -