Donkin's differential operators for homogeneous harmonic functions

Mathematical physics

The work continues the study of the Donkin’s operators for homogeneous harmonic functions. Previously, a basic list of such first-order operators for three-dimensional harmonic functions was obtained. The objective of this study is to prove that any linear combinations with constant coefficients made up of the Donkin’s basic operators are again Donkin’s operators. Since the reversibility property is fundamental for such operators, and since the reversibility of each of the linear differential operators taken separately does not automatically imply the reversibility of their linear combination, this statement is nontrivial and requires a strict proof. This proof has been given in this paper.