BASIC DONKIN'S DIFFERENTIAL OPERATORS FOR HOMOGENEOUS HARMONIC FUNCTIONS

Abstract

It is shown that there are the differential operators that transform three-dimensional homogeneous harmonic functions into new three-dimensional homogeneous harmonic functions. A characteristic feature of these operators is their reversibility: for any homogeneous harmonic function there is a homogeneous and harmonic prototype from which it can be obtained by applying the specified operator. The said operators are named by the authors as differential Donkin operators. The paper provides a complete list of fundamental first order Donkin’ differential operators which form a linear basis of Thomson formulas for three-dimensional homogeneous harmonic functions.

Keywords

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