DONKIN'S DIFFERENTIAL OPERATORS FOR HOMOGENEOUS HARMONIC FUNCTIONS

Abstract

The work continues the study of Donkin 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 Donkin basic operators are again Donkin operators. Since the property of reversibility is a fundamental property for such operators, and since the reversibility of each of the linear differential operators separately does not automatically imply the reversibility of their linear combination, this statement is nontrivial and requires strict proof given in this paper.

Keywords

• electrostatic field
• magnetostatic field
• scalar potential
• homogeneous function
• harmonic function