Basic Donkin's differential operators for homogeneous harmonic functions

Mathematical physics

It has been shown that there are differential operators transforming the three-dimensional homogeneous harmonic functions into new three-dimensional ones. 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 involved operators were called differential Donkin’s operators by the authors. The paper provides a complete list of fundamental first-order Donkin’s differential operators forming a linear basis of Thomson formulas for three-dimensional homogeneous harmonic functions.